7. Bonus: Prove the following Theorem: The Product and the Sum of the Roots of x² + bx + c = 0. Let ri and r2 be the roots of the quadratic equation x2 + bx + c= 0. then rị· r2 = c and r¡ + r2 = -b. In other words, the product of the roots of the equation is the constant term of the equation and the sum of the roots is the negative of the coefficient of the x-term.

Q: How do I complete the square on thsi following polynomial: x2-6x+12-y=0 To end up with:…

A: x2-6x+12-y=0 cannot be expressed as (x-3)2+4-y=0 because (x-3)2+4-y=0 when expanded will give…

Q: Use the Intermediate Value Theorem and Rolle’s Theorem to prove that the equation has exactly one…

A: In the given question, it is required to use Intermediate Value Theorem and Rolle’s Theorem.

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Q: Show that the equation x - 17x + c = 0 has at most one root in the interval [-2, 2].

A: Any function y = f(x) will have exactly one real root in an interval if the function is either…

Q: Find the formula, in standard form y=ax2+bx+cy=ax2+bx+c, for a quadratic that has roots at x = -3…

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Q: I Without solving, find the sum and product of the roots of each of the followine equations. 1. 4x…

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Q: 2. Find the roots of 3x -9x + 2 = 0. Solution: 3x2- 9x = 3(x2-3x + 19 3(x-, 4. X1 =- and X2 = 2. 3I2

A: To find: the roots of the given equation

Q: 1. Find the quotient of x3 −5x2 −2x+ 24  by x−4, and then divide the quotient by x−3. What are the…

A: x-4x2-x-6x3-5x2-2x+24-x3∓4x2-x2-2x+24∓x2±4x-6x+24-6x+2400    ∴x3-5x-2x+24=x2-x-6 x-4 —∗…

Q: 4. What are the roots of the quadratic function y =-x +3x-4? A x+1 and x=-4 x--1 and x-4 315i 3 7 3…

A: Shri Dharacharya method is to be used here

Q: Expand (x + 4)(x – 5) and use this answer to write down the quadratic equation in the form ax2 + bx…

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Q: 10. Write the sustem of lineor equations in the form Arebuand solve this motrit equat 2と, X, t Xu-9…

A: Given: 2x1  -x2 +x4 =93x2 -x3 -x4 =-9x1 +x3 -3x4 =-2x1 +x2 +2x3 =0 To find : x1x2x3x4 for system of…

Q: Practice question 27

A: Find the exact solution of the equation

Q: 14. The condition for the quadratic cquation x2 + 2kx + (k + 6) = 0 to have two uncqual real roots…

A: When a quadratic equation have two real unequal real roots then the value of discriminate is greater…

Q: The intermediate value theorem can be used to prove that the equation x^2+7x+6=0 has at least one…

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Q: 11. Without solving, determine the number of real solutions for each quadratic equation. Show work.…

A: Given:- a) 5q²-3q-6=0 b) 3y²-5y +9=0  To find:- Number of real roots of given quadratic equations

Q: 4) a) Show that the equation y = x³ + 3x2 + 16 has exactly one real root. What is it

A: To show That the equation y=x^3+3x^2+16 has exactly one real root.

Q: 8. For every quadratic there are two roots (or zeroes or x-intercepts). They are always given by Vb²…

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Q: quadratic equation

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Q: solve by demoviers theorem x^7 -i =0

A: ( Cos x+ i sin x )n = cos nx+ I sin nx

Q: If the roots of equation x² - 2cx + ab = 0 a the that th of 2 20 41

A:

Q: We've learned that the roots of the quadratic equation ах+bx+с-0 are given by the quadratic formula…

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Q: If the roots of equation x² - 2cx + ab = 0 are real and unequal, - then prove that the roots of x²…

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Q: Show that in general,the sum of the roots of a quadratic equation ax^2+bx+c=0 is −b/a whereas the…

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Q: Given that f(x) = 12x' - 32x2 + 3x + 5, obtain signs of f(-1), f(0). f(1), f(3) and deduce that…

A: Given that f(x)=12x3-32x2+3x+5 Let us find the signs of f(-1); f(0); f(1); f(3)…

Q: Develop a C program that computes the different roots in a quadratic equation, ax + bX²=0. r = -b ±…

A: we need to compile a C program in order to find the roots of a quadratic equation

Q: (4) Show that in general, the sum of the roots of a quadratic equation ax2 + bx + c = 0 is --…

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Q: 3. Use the Intermediate Value Theorem to show that there is a solution of the equation, ³-4x = 1 in…

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Q: 29 Find all the solutions for the equation below. 1 5 (x – 3) + 11x = (15х — 3) 3 - - - ||

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Q: - (b) Without extracting the roots, determine which one is greater, VII-5 or, 19 – /13.

A: Solution

Q: 6. Show that the quadratic equation ax² + b – a = 0 (a± 0) has two distinct real roots.

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Q: To prove the equation r + z –1=0 has exactly one real root, %3D

A:

Q: Solve for all solutions to 2cos 2t = v3 %3D

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Q: This question must be solved by "the quadratic formula". Be sure to show your work accordingly. 21 +…

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Q: Show that the equation x3 - 17x + c = 0 has at most one root in the interval [-2, 2].

A:

Q: what is the factored form of ax^2+bx+c where the roots are x1 and x2?

A:

Q: 4. Solve for the value of x in equation 4x + 8x 0. A. x 0,-2 B. x 2,-2 C. x 1,2 D. x =-1,-2 5. In…

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Q: Solve for x, where x is a real number. 7x+39 x+30 =3 - (If there is more than one solution, separate…

A: Given equation7x+39-x+30=3We have to solve for x , where x is real number .

Q: A classic example of the quadratic equation in Babylonian mathematics is found on a tablet in the…

A: Step:- 1 a; b is way of writing number in Babylonian mathematics in base 60 to calculate this number…

Q: Let A and B be real numbers such that a root of the equation z ^ 3 + Az ^ 2 + Bz + 26 = 0 is 1 + i.…

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Q: What is rhe third root of unity ?

A: This question can be solved using the concept of complex numbers.

Q: Advanced Math Question

A: To answer the given question we shall use the following rule. Descartes' Rule: The number of…

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A: .

Q: 2. Use the quadratic formula to find the roots of the equation: 5x - 4x +8 = 0. -4+ 12i 5. O x = 3…

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Q: 1. Find how many real solutions x2 + 6x + 24 has. What are those solutions (real or otherwise)?

A: Since you have posted multiple questions as per our guidelines we are allowed to answer the first…

Q: (4) Show that in general, the sum of the roots of a quadratic equation ax? + bx + c = 0 is whereas…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: b) The polynomi al PGX) =x"+mx²+42x²+nx+65, where m and n are real, has zeros 3+2i and 1-i. :) Write…

A: Kindly note that there is misprint in question which is mentioned at the end of solution.

Q: Show that the equation x3 –- 15x + c = 0 has at most one real root in the interval [-2, 2]. |

A: