the graph of a quadratic function written in the form, at the point (h , k) where h and k are given by, + b x + c = 0 has one solution and the graph of f(x) = a x, + b x + c = 0 has two real solutions and the graph of f(x) = a x, + b x + c = 0 has two complex solutions and the graph of f(x) = a x. where x is the amount ( in thousands of dollars) the company spends on advertising. WebTo find the coordinates of the point of intersections of the graphs of f(x) = x 2 + x + c and y = 2 x, we need to solve the system y = x 2 + x + c and y = 2 x which by substitution , gives the equation x 2 + x + c = 2x Rewrite the above equation in standard form x 2 - x + c = 0 Find the discriminant D D = 1 - 4 c Find Vertex and Intercepts of Quadratic Functions - Calculator: Solver to Analyze and Graph a Quadratic Function. If the linear equation is given in the form y = m * x + b, just set x to zero and solve. WebThe moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration.It depends on You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C. WebA first-order differential equation is defined by an equation: dy/dx =f (x,y) of two variables x and y with its function f(x,y) defined on a region in the xy-plane.It has only the first derivative dy/dx so that the equation is of the first order and no higher-order derivatives exist. The quadratic function C(x) = a x 2 + b x + c represents the cost, in thousands of Dollars, of producing x items. WebDifferential Equations Calculator Get detailed solutions to your math problems with our Differential Equations step-by-step calculator. Also, register now to access numerous video lessons for different math concepts to learn in a more effective and engaging way. Our goal is to make science relevant and fun for everyone. For example, in: All terms are in the proper place and form, because y has a coefficient of 1. Example 3 . Polynomial x^{2}+2x+4 is not factored since it does not have any rational roots. To use the direct factoring method, the equation must be in the form x^2+Bx+C=0. Check out all of our online calculators here! We need to calculate $du$, we can do that by deriving the equation above, Substituting $u$ and $dx$ in the integral and simplify, Take the constant $\frac{1}{5}$ out of the integral, Apply the integral of the sine function: $\int\sin(x)dx=-\cos(x)$, Replace $u$ with the value that we assigned to it in the beginning: $5x$, Solve the integral $\int\sin\left(5x\right)dx$ and replace the result in the differential equation, As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$. WebThe height is defined in terms of the width, so I'll pick a variable for "width", b 60, and c 147. t So, t. 3.39 or t. This is a quadratic equation, rewrite it in standard form. Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0. Now solve the equation x=\frac{-46}{2} when is plus. C(x) has a minimum value of 120 thousands for x = 2000 and the fixed cost is equal to 200 thousands. c) no points of intersection. Factor out common term x^{2}-1 by using distributive property. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. Express r and s with respect to variable u. The slope b in this instance is simply 7. Solution to Problem 6. Webhas a slope 1/4 and a y-intercept -2. Then solve the equation L y = b for y. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right). Let's define a variable $u$ and assign it to the choosen part, Now, in order to rewrite $dx$ in terms of $du$, we need to find the derivative of $u$. so that the highest point the object can reach is 300 feet above ground. Consider x^{3}-8. Some of our partners may process your data as a part of their legitimate business interest without asking for consent. 4.. An online LU matrix decomposition calculator is included and may be used to check the solutions and answers below. the terms having the same variable and power. This cannot be simplified. Click Start Quiz to begin! Required fields are marked *, A polynomial is an expression that consists of variables (or indeterminate), terms, exponents and constants. x=\frac{-4\sqrt{16-4\left(-5\right)}}{2}. Group the terms of the differential equation. Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. The quadratic formula gives two solutions, one when is addition and one when it is subtraction. Factor out common term x-1 by using distributive property. , .., x and constant term respectively and it should belong to real number ( R). Factor the expression by grouping. You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C. Find the coefficients a,b and c. Therefore, division of these polynomial do not result in a Polynomial. WebStandards Documents High School Mathematics Standards; Coordinate Algebra and Algebra I Crosswalk; Analytic Geometry and Geometry Crosswalk; New Mathematics Course
, To solve for unknown quantity u, substitute these in the product equation rs = -5, Simplify by expanding (a -b) (a + b) = a^2 b^2, Simplify the expression by subtracting 4 on both sides, Simplify the expression by multiplying -1 on both sides and take the square root to obtain the value of unknown variable u. The y-intercept, b is therefore 7. Identify the values of a, b, Quadratic Equation Calculator Input MUST have the format: AX 2 + BX + C = 0 EXAMPLE () + ()! Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. WebGet breaking NBA Basketball News, our in-depth expert analysis, latest rumors and follow your favorite sports, leagues and teams with our live updates. Your Mobile number and Email id will not be published. Let y = U x. If you already have an equation in this form, finding b is trivial. Factor out x in the first and 5 in the second group. Note that B here is not the same as b above. Step 1: Divide All Terms in the Equation by B. Its distance S(t), in feet, above ground is given by. If x^2 or y^2 terms appear, try to collect them on one side of the equation. Now solve the equation x=\frac{-46}{2} when is minus. First, we must identify a section within the integral with a new variable (let's call it $u$), which when substituted makes the integral easier. https://math.stackexchange.com/questions/1984114/on-a-polynomial-with-roots-in-1-3-that-are-also-of-the-form-2-csc-theta, https://socratic.org/questions/56e382a47c014915a4b08b44, https://math.stackexchange.com/questions/1477117/determine-the-exact-value-of-sin-theta-cos-theta-if-csc-theta-3, https://socratic.org/questions/how-do-you-find-the-values-of-the-six-trigonometric-functions-given-csctheta-4-a, https://socratic.org/questions/how-do-you-use-csctheta-5-to-find-cottheta, https://math.stackexchange.com/questions/1189707/how-to-explain-that-int-frac-sec-theta-tan2-thetad-theta-is-equal-to, \frac{\mathrm{d}}{\mathrm{d}\theta }(\frac{1}{\sin(\theta )}), \frac{\sin(\theta )\frac{\mathrm{d}}{\mathrm{d}\theta }(1)-\frac{\mathrm{d}}{\mathrm{d}\theta }(\sin(\theta ))}{\left(\sin(\theta )\right)^{2}}. 2022. Solution We first solve for y in terms of x by adding -2x to each member. Solution to Problem 5, Problem 6 WebAlgebra with pizzazz worksheet answers 101, quadratic equation extremum, algebra like terms worksheets, how to work out 2004 maths sats paper KS3, Kumon work sheets, "free online algebra calculator". Web- Rewrite Y is equal to 2/3x plus 4/7 in standard form. The consent submitted will only be used for data processing originating from this website. The values of r and s are equidistant from the center by an unknown quantity u. Practice your math skills and learn step by step with our math solver. The factors r and s are the solutions to the quadratic equation. WebThis means the variable terms are not squared (such as x^2 or y^2) or some higher power. \left(-\frac{1}{\sin(\theta )}\right)\times \left(\frac{\cos(\theta )}{\sin(\theta )}\right). Examples with Solutions Example 1 Find the L U composition of matrix A = [ 1 1 2 1] . For any two differentiable functions, the derivative of the quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared. "Sinc The differential equation in first-order can also be written as; A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable). Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. An example of a polynomial with one variable is Solution to Problem 3, Problem 4 You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C. The profit (in thousands of dollars) of a company is given by. Quadratic equations such as this one can be solved by a new direct factoring method that does not require guess work. Do the grouping x^{5}-x^{3}-8x^{2}+8=\left(x^{5}-x^{3}\right)+\left(-8x^{2}+8\right), and factor out x^{3} in the first and -8 in the second group. WebExample: 1 Consider the expression: $$4x + y.$$. Repeat steps 2 to 4 until you have no more terms to carry down. Calculator simple exponents and fractional exponents WebGet 247 customer support help when you place a homework help service order with us. Check out all of our online calculators here! WebTwo-step equation calculator, 7th grade algebra help, linear equation java code, missing ordinal numbers worksheet, algebra help AND world problems, free online math problem solver for 3 graders. The values of r and s are equidistant from the center by an unknown quantity u. Select the correct answer and click on the Finish buttonCheck your score and answers at the end of the quiz, Visit BYJUS for all Maths related queries and study materials, I am doing algebra at school , and I forgot alot about it. Examples with Solutions Example 1 Find the L U composition of matrix A = [ 1 1 2 1] . WebIntegrals by Partial Fraction expansion Calculator Get detailed solutions to your math problems with our Integrals by Partial Fraction expansion step-by-step calculator. ins.style.display='block';ins.style.minWidth=container.attributes.ezaw.value+'px';ins.style.width='100%';ins.style.height=container.attributes.ezah.value+'px';container.appendChild(ins);(adsbygoogle=window.adsbygoogle||[]).push({});window.ezoSTPixelAdd(slotId,'stat_source_id',44);window.ezoSTPixelAdd(slotId,'adsensetype',1);var lo=new MutationObserver(window.ezaslEvent);lo.observe(document.getElementById(slotId+'-asloaded'),{attributes:true}); If a > 0, the vertex is a minimum point and the minimum value of the quadratic function f is equal to k. This minimum value occurs at x = h. Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). To add polynomials, always add the like terms, i.e. Free online calculators for exponents, math, fractions, factoring, plane geometry, solid geometry, algebra, finance and more. Rewrite x^{2}+4x-5 as \left(x^{2}-x\right)+\left(5x-5\right). The values of r and s are equidistant from the center by an unknown quantity u. WebFast Company is the world's leading progressive business media brand, with a unique editorial focus on innovation in technology, leadership, and design. Say you have an equation: This reduces the coefficient of y to 1, as desired. Solve the equation using the Quadratic Formula. Let me get my scratch pad out. In this example, there are three terms: x, The word polynomial is derived from the Greek words poly means . WebTwo numbers r and s sum up to -2 exactly when the average of the two numbers is \frac{1}{2}*-2 = -1. Find the equation of the tangent line to the the graph of f(x) = - x 2 + x - 2 at x = 1. Since ab is negative, a and b have the opposite signs. Find the slope and y-intercept of 2x - 3y = 6. Substitute 1 for x_{1} and -5 for x_{2}. Will calculate the value of the exponent. WebDefinition. WebWe can pretty easily translate an equation from slope intercept form into standard form. Access detailed step by step solutions to thousands of problems, growing every day! Find values of the parameter m so that the graph of the quadratic function f given by, Problem 5 Example: 2 To simplify an expression $$4x^2 + 3x + 4y + 8x + 9x^2$$. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right). Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. Non-Linear Differential Equation Often, however, an equation that can ultimately be represented in this form appears in disguise. y) at which the the line crosses the y, or vertical, axis. b) 1 point of intersection, Write the polynomial in descending order. the k represents a vertical shift (how far up, or down, the graph has shifted from y = 0). Note the final answer, including remainder, will be in the fraction form (last subtract term). therefore I wanna some help, Its good it helped me very much for my project, Your Mobile number and Email id will not be published. Rewrite the complete factored expression. We will guide you on how to place your essay help, proofreading and editing your draft fixing the grammar, spelling, or formatting of your paper easily and cheaply. x=\frac{-4\sqrt{4^{2}-4\left(-5\right)}}{2}. We will use a new variable y = x(20p + x). 30. Math Questions With Answers (13): Quadratic Functions. It is possible to solve equations with x^2 and y^2 terms by the same methods we have used so far. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. have: Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. If the linear equation is given in the form y = m * x + b, just set x to zero and solve. For example, dy/dx = 5x WebSolve your math problems using our free math solver with step-by-step solutions. About the Author. WebThis will yield the equation (LU)x = b. The quadratic function f(x) = a x 2 + b x + c can be written in vertex form as follows: if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[580,400],'analyzemath_com-box-4','ezslot_5',260,'0','0'])};__ez_fad_position('div-gpt-ad-analyzemath_com-box-4-0'); Problem 1 The equation must be simplified, which means all numbers must be integers that do not share a common factor other than one. We and our partners use cookies to Store and/or access information on a device.We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development.An example of data being processed may be a unique identifier stored in a cookie. WebSolve your math problems using our free math solver with step-by-step solutions. $\left(1+x^4\right)\cdot dy+x\cdot\left(1+4y^2\right)\cdot dx=0$, $\frac{dy}{dx}=\frac{3x^2+4x+2}{2\left(y+1\right)}$. The degree of zero polynomial is not defined while the degree of a constant polynomial is 1. Use the answer in step 2 as the division symbol. notice that the h value is subtracted in this form, and that the k value is added. Rewrite y = 2x - 6 in standard form. The addition of polynomials always results in a polynomial of the same degree. a) 2 points of intersection, WebThis will yield the equation (LU)x = b. 6. m is the slope, or tilt, of the line on the graph, whereas b is the y-intercept, or the point (0. $\exponential{x}{5} - \exponential{x}{3} - 8 \exponential{x}{2} + 8 $. 2022. Simplify all the expressions of the form p-\left(-q\right) to p+q. If a < 0, the vertex is a maximum point and the maximum value of the quadratic function f is equal to k. This maximum value occurs at x = h. () +,where n! Problem 2 Check the highest power and divide the terms by the same. Put your understanding of this concept to test by answering a few MCQs. Substitute the value of u to compute the r and s. x^{2}+4x-5=\left(x-1\right)\left(x+5\right). To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. Question 2 The derivative of the constant 1 is 0, and the derivative of sin(\theta ) is cos(\theta ). WebAlso, the differential equation of the form, dy/dx + Py = Q, is a first-order linear differential equation where P and Q are either constants or functions of y (independent variable) only. But sometimes, a few steps are required to get there. WebQuadratic equation calculator shows work, equation of elipse, grade 10 factors help, triginometry calculator, lcm excel formula, softmath, java input in bold. Following a bumpy launch week that saw frequent server trouble and bloated player queues, Blizzard has announced that over 25 million Overwatch 2 players have logged on in its first 10 days. WebSolve your math problems using our free math solver with step-by-step solutions. Due to the fact that x and y are different variables, this expression cannot be simplified. Prop 30 is supported by a coalition including CalFire Firefighters, the American Lung Association, environmental organizations, electrical workers and businesses that want to improve Californias air quality by fighting and preventing wildfires and reducing air pollution from vehicles. Practice your math skills and learn step by step with our math solver. if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[580,400],'analyzemath_com-banner-1','ezslot_8',360,'0','0'])};__ez_fad_position('div-gpt-ad-analyzemath_com-banner-1-0'); Problem 3 A = 4 Oa y.dx. For example, 3x, A standard polynomial is the one where the highest degree is the first term, and subsequently, the other terms come. An object is thrown vertically upward with an initial velocity of Vo feet/sec. Find values of the parameter c so that the graphs of the quadratic function f given by Find the equation of the quadratic function f whose graph passes through the point (2 , -8) and has x intercepts at (1 , 0) and (-2 , 0). The Taylor series of a real or complex-valued function f (x) that is infinitely differentiable at a real or complex number a is the power series + ()! Enter the non negative of the quadrant of a circle can be calculated by the method of integration used for calculating area under the curve.The equation of the curve is y = (a 2 - x 2) and the limit is from O to a. Ti-89 dirac delta function, solving literal equations worksheet, multiplying and simplifying calculator, Help with KS3 maths algebra negative numbers. To find linear differential equations solution, we have to derive the general form or representation of the solution. and the graph of the line whose equation is given by y = 2 x Solution to Example 1. WebIt can do almost any integral that can be done in terms of standard Rewrite Triple Integral Calculator. So it's Y is equal to 2/3x plus 4/7. Manage SettingsContinue with Recommended Cookies. Solution: Collect and add the like terms which gives; $$9x^2 + 4x^2+ 8x + 3x + 4y => 13x^2 + 11x + 4y.$$ Based on this example, we can conclude that Determine the greatest digit x such that (+). WebWe would like to show you a description here but the site wont allow us. To find a and b, set up a system to be solved. \left(-\csc(\theta )\right)\times \left(\frac{\cos(\theta )}{\sin(\theta )}\right). var cid='7714110523';var pid='ca-pub-8886524782132322';var slotId='div-gpt-ad-analyzemath_com-medrectangle-3-0';var ffid=1;var alS=1021%1000;var container=document.getElementById(slotId);container.style.width='100%';var ins=document.createElement('ins');ins.id=slotId+'-asloaded';ins.className='adsbygoogle ezasloaded';ins.dataset.adClient=pid;ins.dataset.adChannel=cid;if(ffid==2){ins.dataset.fullWidthResponsive='true';} All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b\sqrt{b^{2}-4ac}}{2a}. 30. 3. Rewrite the quotient as a product of two quotients. Let y = U x. Rewrite x^{2}-1 as x^{2}-1^{2}. WebRsidence officielle des rois de France, le chteau de Versailles et ses jardins comptent parmi les plus illustres monuments du patrimoine mondial et constituent la plus complte ralisation de lart franais du XVIIe sicle. WebAbout Our Coalition. x 2 + y 2 xy and xy + yx are examples of homogenous differential equations. Microsoft pleaded for its deal on the day of the Phase 2 decision last month, but now the gloves are well and truly off. Then solve the equation L y = b for y. 6. WebFind p, y and x, as follows: Let p be the part of the root found so far, ignoring any decimal point. Consider x^{2}-1. Rewrite x^{3}-8 as x^{3}-2^{3}. WebA differential equation in which the degrees of all the terms is the same is known as a homogenous differential equation. WebSolve Exponential Equations for Exponents using X = log(B) / log(A). (5s2+2s+1). (),where f (n) (a) denotes the n th derivative of f evaluated at the point a. 4.. An online LU matrix decomposition calculator is included and may be used to check the solutions and answers below. Webwithout solving the equation or factoring, determine the solution to the equation -9, using only the graph ; ti 89 complete square ; Holt, Rinehart and Winston worksheet answers for Skills worksheet section: Scientific Methods ; multiplying integers with parenthesis ; slope and y-intercept calculator ; slope intercept form solving on ti-84 The only such pair is the system solution. https://www.tiger-algebra.com/drill/x~3-8x~2_12x=0/, https://www.tiger-algebra.com/drill/x~3-8x~2_17x-6/, http://www.tiger-algebra.com/drill/x~3-8x~2-x_8=0/, https://www.tiger-algebra.com/drill/x~5-2x~3-x~2_2/, https://www.tiger-algebra.com/drill/x~5-4x~3-x~2_4/, https://www.tiger-algebra.com/drill/x~5-9x~3-x~2_9/, x^{3}\left(x^{2}-1\right)-8\left(x^{2}-1\right). and the graph of the line whose equation is given by. Whether you need help solving quadratic equations, inspiration for the upcoming science fair or the latest update on a major storm, Sciencing is here to help. \frac{6x - 3y}{3} = \frac{21}{3} \\ \,\\ 2x - y = 7, -y = 7 + 2x \\ y = -7 - 2x \\ y = -2x -7 \\, 6x -3y = 21 \\ (6 0) - (3 -7) = 21 \\ 0 + 21 = 21, MathCentral: Converting y=mx+b into ax+by+c=0 and Vice Versa, Math: Basic Equations of Lines and Planes. WebDifferential Equation Definition. Solution to Example 1. It represents a linear equation, the graph of which, as the name suggests, is a straight line on the x-, y-coordinate system. WebTwo numbers r and s sum up to -7 exactly when the average of the two numbers is \frac{1}{2}*-7 = -\frac{7}{2}. is for ease of graphing. Alright, we'll worry about this second part in a little bit. WebThe moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration.It depends on First, the expression needs to be rewritten as x^{2}+ax+bx-5. Rewriting Equations in Standard Form. Since a+b is positive, the positive number has greater absolute value than the negative. (For the first step, p = 0.) Standard Form: Ax + By = C. This means that we want the variables (x & y) to be on the left-hand side and the constant (6) to be on the right-hand side. 2022 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. Let's see if we can rewrite this. \left(x-2\right)\left(x-1\right)\left(x+1\right)\left(x^{2}+2x+4\right). () + ()! As it happens, any equation that can appear as: where A, B and C are constants, x is the independent variable and y is the dependent variable is a linear equation. Subtract 6 from -4. x^{2}+4x-5=\left(x-1\right)\left(x-\left(-5\right)\right). WebWhen written in "vertex form ": (h, k) is the vertex of the parabola, and x = h is the axis of symmetry. f(x) = x 2 + x + c For example, x. More about Kevin and links to his professional work can be found at www.kemibe.com. Note: 20p + x is simply twice Move the terms of the $y$ variable to the left side, and the terms of the $x$ variable to the right side of the equality, Integrate both sides of the differential equation, the left side with respect to $y$, and the right side with respect to $x$, The integral of a constant is equal to the constant times the integral's variable, Solve the integral $\int1dy$ and replace the result in the differential equation, We can solve the integral $\int\sin\left(5x\right)dx$ by applying integration by substitution method (also called U-Substitution). quadratic functions problems with detailed solutions are presented along with graphical interpretations of the solutions. If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page. -\frac{\cos(\theta )}{\left(\sin(\theta )\right)^{2}}. If an equation is not written in x = mx + b form and we want to know the slope and/or the y-intercept, we rewrite the equation by solving for y in terms of x. The values of r and s are equidistant from the center by an unknown quantity u. +x-12. WebTwo numbers r and s sum up to -4 exactly when the average of the two numbers is \frac{1}{2}*-4 = -2. 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The formula y = mx + b is an algebra classic. y + x(dy/dx) = 0 is a homogenous differential equation of degree 1. x 4 + y 4 (dy/dx) = 0 is a homogenous differential equation of degree 4. You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C. dy/dx = f(x) Here x is an independent variable and y is a dependent variable. Keep visiting BYJUS to get more such math lessons on different topics. We see that $5x$ it's a good candidate for substitution. Now subtract it and bring down the next term. Variables are also sometimes called indeterminates. denotes the factorial of n.In the more compact sigma notation, this can be written as = ()! Let r and s be the factors for the quadratic equation such that x^2+Bx+C=(xr)(xs) where sum of factors (r+s)=B and the product of factors rs = C, Two numbers r and s sum up to -4 exactly when the average of the two numbers is \frac{1}{2}*-4 = -2. 3. Add -4 to 6. 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