1. Factoring is used to solve quadratics of the form ax? +bx +c=0 when the roots are rational. Find the roots of the following quadratic functions by factoring: a. f(x) = x² - 5x –14 b. f(x) = x2 -64 c. f(x) = 6x² +7x-3

Q: Find the roots of 2x2-2(√2x) +1=0,If they  exist using quadratic formula

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Q: Discuss the nature of the quadratic form x2+4xy+6xz-y2+2yz+4z2

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Q: Find all the solutions to the polynomial: x* + 4x°+7x² + 16x + 12 = 0 1 -4 -2i O 2i -3 O -1

A: A polynomial function is a function that involves only non-negative integer powers or only positive…

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

A: For solving a polynomial equation put

Q: Show that there is a root of the equation x3 - x - 1 = 0 between 1 and 2.

A: Consider the given equation. x3-x-1=0 and, fx=x3-x-1 Put x=1 in the function. f1=13-1-1=-1

Q: The solution of the quadratic equation 5æ? + 5x + 1= 0 are -5 + V15 15 O -5± V15 10 O -5 + /15 20 O…

A: A detailed solution is given below

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.

Q: 29. Select the quadratic polynomial with roots -1 and 4. 22 + 3x – 4 O a3 – 2a? – 7æ – 4 O 4x2 + 8x…

A: It is given that the equation is in quadratic And the two roots of the equations are -1 , 4    This…

Q: Show that the product of the roots of a quadratic equation is c/a .

A: Consider the quadratic equation ax2+bx+c=0 Also consider that α and β are the roots of the quadratic…

Q: Find the real solutions of each quadratic equation: (a) 5x2 + 5x = 1 - 5x2 (b) 2x2 - 8x - 10 = 0…

A: Answer is mentioned below

Q: The solutions to Shana's quadratic equation are x = 3 and I = . Which could be Shana's equation?…

A: Just write the form of quadratic equation when its solution is given.

Q: Solve the quadratic equations by using any method of solving quadratic equations. 1. x2-2x-35%-D0 6.…

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Q: Whatis the value of r in the quadratic equation x? – 10x –r= 0 whose roots are equal rational and…

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Q: Show that the equation x4 + 4x + c = 0 has at most two real roots

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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: 49 Find a quadratic equation with integer coefficients whose roots are the reciprocals of 4x2 - 23x…

A: We have to find a quadratic equation whose roots are reciprocal to roots of given equation- given…

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: 15. Given the equation 3x-4x -12 =0, how many roots are there? Rational or irrational?

A: Given equation  3x2-4x-12 = 0 ....... (1) Quadratic formula for the solution of the quadratic…

Q: Solve the quadratic by looking at the graph. 10+ 4 2 10 -9 8 -7 6 -5 4 -3 -2 -1 i 2 345 67 8 9 1c

A: Given:

Q: & and ß are the roots of a quadratic equation such that a + B = 2 and aß =. The value 3. *of a' + B?…

A: we have to find the following

Q: quadratic equation

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Q: What is the equation of a quadratic in standard form, given the zeros x = 3 and x = 6 and the point…

A: The solution is given below.

Q: Solve 6x^2-2x+1=0 using the quadratic formula while find both of the Xs. (Show work)

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Q: Use the quadratic formula to solve for x. 9x+ 5x–1=0 (If there is more than one solution, separate…

A: We have given equation 9x2+5x-1=0 Then, comparing this ax2+bx+c=0 we have a=9,b=5,c=-1 Now, using…

Q: Suppose x=−3−9i  is a solution of a quadratic equation with real coefficients. Then another…

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Q: Find the quadratic function using the given roots 1. (-3 2 ,0) and (1,0) 2. (2 3 ,0) and (-3,0)

A: We can find the quadratic functions as below.

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: 4. Use the quadratic formula to find the zeros of each function. a. f(x) = 3x² + 5x – 2 %3D b. f(x)…

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Q: Prove that the equation 2x2 + y² 14 has no positive integer solutions.

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Q: Find the discriminant of the quadratic equation and give the number and type of solutions of the…

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Q: Use the quadratic formula to find the exact and approximate solution. Round to 3 decimal places.…

A: Given,          y=-2x2+2x+5We know that,       The quadratic formula for the equation ax2+bx+c=0 ,…

Q: 1. Use what you have learned to solve the following polynomial equation by either completing the…

A: To solve given polynomial equation: Here, By using the quadratic formula, ax2+bx+c=0 x = -b…

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

A: We have to solve given problem:

Q: Show that the equation 6x4 – 7x +1 = 0 does not have more than two distinct real roots.

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Q: 8.) Solve the given quadratic equation using the factoring method. x² +5x+2 = -2x² +7x+7

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Q: The solutions of the quadratic equation x(4x – 3) + 3 = 0 are - O None of these O 3±iv57 8. O…

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Q: Show that the equation r1 + x³ + 4x – 2 = 0 has exactly one real root.

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

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Q: Write the quadratic formula root [-6+v6? – 4ac]/(2a) in a form so that there are no serious problems…

A: Given: The quadratic formula root, -b+b2-4ac2a b is positive and very large compared to ac. Find:…

Q: e and p are the roots of the quadratic equation x2+ 5x– 13 = 0, form a quadratic equation in x whose…

A: Given,            α and β are the roots of the quadratic equation x2 + 5x - 13 =0

Q: 5. Algebraically find the x-intercepts of the quadratic function whose equation is y=x² – 4x – 6.…

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Q: Given the quadratic function y = x2 + 8x + c , where c is some real number constant, answer the…

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Q: Whatis the value of r in the quadratic equation x² – 10x – r = 0 whose roots are equal rational and…

A: .

Q: Use the Quadratic formula to find TWO solutions to 2x2+ 3x – 10 =0. sSelect them from the choices…

A: Solution:

Q: Find the value of k in the equation x2 – 3x + k = 0 if its roots are real, irrational and not equal.

A: Since you have multiple questions in a single request. we would be answeringonly the first question…

Q: If a and 3 are the roots of the quadratic 3x2 – 4x + 6 = 0, find the value of

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

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

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Q: it is given that α and β are the roots of quadratic equation 2x^2-5x+6=0.Form a quadratic equation…

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Q: The solutions of the quadratic equation x + 3x + 9 = 0 are O -3+iv36 2 -3+iv27 2 O -3+iv27 4 O…

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