For what value of a will five of the six real roots of 6x6 + 7x5 _ 43z4 - 153 + 49z2 + ax polynomial 2x5 + x4 - 15x3 +5x2 + 13x - 6? 12 be shared by the

Q: Confirm that 2 is an upper bound and -15 is a lower bound for the real zeros of f(x) = x* + 14x3 +…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The polynomial + ax 3x+ hx 2 has roots -1 and 2. one of which is a triple root. Find the values of a…

A: There are two possible case, checking one by one both to know which is the possible case as in next…

Q: Find the root of 4x³ +3x² + 2x +11 over the interval [-2,–1].

A: We will find out the required root.

Q: Verify the factorization by using synthetic division 3x3 - 5a2-4x + 4 = 3(x+ 1)(x– 2)(x –) Verify…

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Q: Show that (x- 3) is a factor of 2.x3 - 2x2 - 17x + 15. Hence express 2x³ – 2.x² – 17x + 15 in the…

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Q: give all the possible roots of x4+2x3-7x2-8x+12

A: Give all the possible roots of x4+2x3-7x2-8x+12

Q: Determine all the roots the following polynomial 24 – 2z3 + 10z² – 18z + 9 if one of the root is -j3

A:

Q: )without actually obbinig thex roots, show that x6-Sx -7x²+8x+20=0 roots a) x° +3 xt=6 buth possess…

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Q: Show that x2 + 3x + 2 has four zeros in Z6.

A:

Q: how many roots does -2x^(2)+8x^(9)-10x^(5)+12 have?

A: Roots of a polynomial are determined by its degree. Degree = highest power of x in the given…

Q: ind a polynomial p(x) with zeros as -2,-3,1,3 ?

A: To find a polynomial p(x) with zeros as -2,-3,1,3

Q: express 5x2 - 3x + 6 in terms of Legendre's polynomial.

A:

Q: Express as a polynomial. (r 2 + 8r - 2-)(r 2 + 3r - 1)

A: Given expression:                         (r2+8r-2)(r2+3r-1)

Q: Select the correct number of roots for each polynomial. 4x2 + x – 1 – 3x+ [Select] | Зх — 8 + 9х […

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Q: Form a quadratic with real coefficients having amongst its roots -6+i

A: As given in this question, one root is imaginary then other will also be an imaginary roots.

Q: Express the area of the polygon as a polynomial. 41. Rectangle 42. Right triangle 6x - 1 4x² - 1…

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Q: Find the least common multiple of the denominators of 1/ (x2 - 1)  and 3/ (x2 + 4x + 3)

A: Given: 1x2-1 and 3x2+4x+3

Q: If a polynomial cannot be written as the product of two other polynomials (excluding 1 and - 1),…

A: We know that a prime number have only 1 and that number as its factors.

Q: Every polynomial equation of the nth degree has n real roots Select one: O True O False

A: Given :   Every polynomial of degree of nth degree has two types of roots : Real and Non-real /…

Q: Ax) = x' - 7x* + 10x + 14x – 24x

A: To determine all the zeros of the given polynomial.fx=x5-7x4+10x3+14x2-24x

Q: Show that x2 − 4 is a factor of x4 − 5x3 + 2x2 + 20x − 24.

A:

Q: 18. Express the polynomial 6x -x +2x-4 in standard form. 6x'-2x-4 7 +2x-4 -4+2x-5x 5x +2x-4

A: standard form is the form in which polynomial is written decreasing power of x and all different…

Q: Prove that 3x3+ 5x - 11 has a root between x=1 and x=2. Thanks!

A:

Q: By what polynomial of lowest degree must (x2 – 64)(x² + 5x – 24) be multiplied to make it a perfect…

A: Givem polynomial is (x2-64)(x2+5x-24)To find lowest degree multiplier to make it perfect square.

Q: 23 – 522 – 9z + 45

A: Given: z3-5z2-9z+45

Q: Find the sum of the polynomials -3x +7x-8 and 5x-7x+2. Subtract -x +5x-3 from 6x2-3x-7. Express the…

A: We can find the answers as below

Q: Show that x2 + 3x + 2 has four zeros in Z6

A:

Q: Solve the polynomials 3y-{[-4(x-y)+(2x - y)]-3x -[(5y-3(x-2y)]-2(-6x + y)}

A: Given polynomial,  3y-{[-4(x-y)+(2x - y)]-3x -[(5y-3(x-2y)]-2(-6x + y)}

Q: If x=9 is a solution to a polynomial equation, then (x-9) will be a factor a that polynomial

A: The given statement is true.

Q: The number of zeros of the polynomial x² + 2x + 3 in Z, is: 2 1 4 None

A: 2

Q: Show that If 2 is a root of  kx4 - 11x3 + kx2 + 13x + 2 Then K = 3

A: Given,          2 is a root of kx4-11x3+kx2+13x+2 then k=3.

Q: Give a polynomial equation with integral coefficients that has the following roots. 0, -3, -1, 2

A: This question is related to polynomials, we will solve it using given information.

Q: Find the least common denominator of[(3/x2 - 6x + 9) and (7/x2 - 9)]

A: Given, expressions, 3x2-6x+9  and   7x2-9

Q: Create a polynomial equation with real coefficients that has 2 and 1-i as roots.

A: To create a polynomial equation with real coefficients that has 2 and 1-i as roots.

Q: Find a real root of 3*exp(-x/2)+4*In(x)-2 = 0 using False Position method with a=0.5 and b=2.0…

A: Given:            3*exp(-x/2)+4*ln(x)-2=0           3·e-x2+4lnx-2=0     By using False position…

Q: 1. Which polynomial has 31, -31, and 3 (with multiplicity 2) as its roots? A -3x' +9x + 27 Bx -6x'…

A:

Q: What are all the possible rational roots of 2x^3 + 3x^2 - 10x + 4 = 0?

A: Given: - The equation is, 2x3+3x2-10x+4=0 To find: - The rational roots of the given equation.

Q: Find the approximate root of x^3+5x-2=0 by using bisection method. Typed solution needed otherwise…

A: Given,            x3+5x-2=0

Q: Determine between which consecutive integers the real zeros of Ax) = 3x - 5x² + 5x +7 are located on…

A: Given : f(x)  =3x3-5x2+5x+7 Interval [ -10 , 10]

Q: x2 - 4 is a factor of x4 - 5x3 + 2x2 + 20x - 24

A:

Q: Find a real root of 4*exp(-x/2)-3*In(x)-3 = 0 using False Position method with a=0.1 and b=2.0…

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Q: Express f(x) = 4x3 + 6x2 + 7x + 2 in term of Legendre Polynomials.

A: The Legendre equation is, 1-x2d2ydx2-2x dydx+nn+1y=0 The polynomial denoted by Pnx is called the…

Q: How can I show that there exists at least one solution in the set of real numbers for x5-x3+3x=5…

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Q: Discuss the possibilities for the roots to : 2x'-5x - 6x+4 = 0 12. 3x - 5x -x² -8x+4 =0

A: We can use Descartes rule of signs to check the nature of possible roots of the given function, P(x)…

Q: List all the possible rational roots of 4x-2x – 6x² + 22x – 15 =0. Show all work.

A: We need to use the rational roots theorem. It says that if we have a polynomial f(x) with integer…

Q: To find the possible roots of the polynomial 4x3 + x4 - 7x² - 8x - 8

A:

Q: Express the polynomial x3 + 2x+3 EZ[x]as a product of irreducible polynomials of 75[x]- Attach File…

A: Use the definition of irreducible polynomial and property of ring Z_5[x].

Q: How can all real zeroes be found for 6x^3 - 24x^2 + 6x?

A: This question can be solved using the concept of finding the zeroes.