1. Which polynomial has 31, -31, and 3 (with multiplicity 2) as its roots? A -3x' +9x + 27 Bx -6x' +54x-81 Cr-6x' + 18x-54x + 81 Dr -6x + 12x-18x + 27

Q: An nth degree polynomial will have at most n+1 real roots. O True O False

A: No, that is not possible. The only reason that an n-degree polynomial has max n roots is that it can…

Q: 2. Use syntr dhe hirst polynomial by the second. а. х2+x -3; х-1 b. 4x- 3x2+ 3x - 2; x-1 c. x'+x°…

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Q: Show that the polynomial 2x + 1 in Z4[x] has a multiplicative inverse in Z4[x].

A:

Q: 10. Write a third-degree polynomial f(x) with integer coefficients and zeros of 5, -, and 4.

A: Let the polynomial is  fx=αx-15x--23x-4=αx-15x+23x-4=α5x-153x+22x-4 Coefficient will be integer if α…

Q: (a) Factorise z° + 1 over the real numbers.

A:

Q: Find a polynomial with integer coefficients that has degree 4 and zeros 1−2i and 1, with 1 a zero of…

A:

Q: Show that the polynomial 2x + 1 in Z4[x] has a multiplicative inversein Z4[x].

A:

Q: polynömial that passes through the three points (0, 1), (1, 2) and (2, 23). If the coefficient of x…

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Q: 4. Write a polynomial to express the total value, T(x), of (x + 4) 20-Peso bills (x – 3) 50-Peso…

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Q: If f(x) is a polynomial with real coefficients and zeros of 5 (multiplicity 2), –1 (multiplicity 1),…

A: The number of zeroes are 4. But one zero has a multiplicity of 2 that is the zero is repeated.

Q: 16. Find a fourth degree polynomial that has the zeros 3, -2, i.

A: Given data: The first root of the polynomial is x1=3. The second root of the polynomial is x2=-2.…

Q: Write a general polynomial q(z) of degree n with coefficients that are bo, b,, b2, ..b,. What are…

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Q: 5. For how many different integers bis the polynomial x² + bx + 16 factorable over the integers?

A: From the given data

Q: find a formula for the polynomial P(x) with degree 3 leading coefficient 2 zeros at -5, -3, and 3

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Q: 6- Show that the Polynomial has a Z4 [x] 2X+1 in multiplicative invers. in 24 [x].

A: Given

Q: Form a polynomial with a Degree 4; zeros:4+2i, -1 multiplicity 2

A:

Q: Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and…

A: Follow the procedure given below.

Q: Find the polynomials connecting the points (0,1), (1,3), and (2,13) ​​by quadratic interpolation.

A:

Q: If f(x) is a polynomial with real coefficients and zeros of 4 (multiplicity 3), –2 (multiplicity 1),…

A: The multiplicity means that the zero of the polynomial is repeating. For example, let's take a…

Q: Find a polynomial f(x) of degree 4 that has the following zeros. 0, 9 (multiplicity 2), -6 Leave…

A:

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: Find a formula for the polynomial P(x) with degree 3  leading coefficient 1 zeros at 8, -6, and 7…

A:

Q: (b) Show that factorial polynomial corresponding to P,- k³ – 4k* + 2k³ – k² + k + 10 is P, = k(5) +…

A: Given: The given polynomials is Pk=k5-4k4+2k3-k2+k+10, To prove Pk=k5+11k4-k3-9k2-k1+10

Q: In the polynomial x^6 − 3x^5 − 5x^4 + 22x^3 − 39x^2 − 39x + 135, it is known that 1 + 2i and √3 are…

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Q: 1. It is known that the polynomial p(x) = 2 – (x + 1) + x(x + 1) – 2æ(x + 1)(x – 1) interpolates the…

A: Solution by using Newton's forward difference interpolation method .

Q: Express the polynomial x3+2x+3 in Z5[x] as a product of irreducible polynomials of Z5[x] .

A: Explanation of the answer is as follows

Q: 1. Determine whether the set S = {2x² – 14x + 34, 3x – 4, x² + 5x + 1} is linearly independent or…

A: Here first we check the set s is linearly dependent or not.

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

A:

Q: Form the polynomial function that has the following real ZEROS: 3,-1, 2, 4 Section 3.1 O z4 + 2z3 -…

A: Given point is; x = -3,-1,2,4   1) x4+2x3-14x2-13x+24  we find the factor of this function and then…

Q: Find a polynomial with integer coefficients that has 1/2 and -1/3 aszeros.

A: Since the required polynomial is to have two zeroes, it's degree should be 2 i.e. It should be a…

Q: Show that the polynomial x5 - 6x + 3 over Q is not solvable byradicals.

A:

Q: Show that the polynomial z5 + 14z + 2 has four zeros in the annulus </2 < 2.

A: Given

Q: D. Find a fourth-degree polynomial with integer coefficients that has zeros 3i and -1, with -1 a…

A: The given zeros are 3i,-3i,-1 and -1.

Q: 1. Find the sum of the polynomials: (5x°-2x+x)+(4x° – 3xª +2x³-5x) O x5 +3x4-4x3+6x O 9x5+3x4-4x³+6x…

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Q: I. Use the Factor Theorem to determine whether the given binomial of the form x - cis a factor of…

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Q: What is the fermat value, in polynomial form, of integer 'a', if a=x^4 + 1; p=x^2 + 1?

A: We have to find the Fermat value 'a' which is given in the following form, a=x4+1p=x2+1

Q: 8. Construct a polynomial with Z coefficents with a root of the given C 3+ V5 (a) (b) 2+ 3і (c) 1-…

A: We have to solve the given problem.

Q: find a degree 3 polynomial having zeros 7, -3, and -8 and leading coefficient equal to 1.

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Q: 1. Write the equation to the polynomial with double roots at 3 and 6, that levels off as it passes…

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Q: 6. Does there exist a polynomial of degree 4 with integer coefficients that has zeroes i, 2i, 3i and…

A: Complex root must be in conjugate pair

Q: Form a polynomial with  the given roots 1+2i, 1-2i , 4 ,2

A:

Q: A fourth-degree polynomial with real coefficients canhave −5, −8i, 4i, and 5 as its zeros.

A: Given the statement that a fourth degree polynomial has real coefficients can have  -5 ,-8i 4i and 5…

Q: Show that the given values for a and b are lower and upper bounds for the real zeros of the…

A: Solution:- Any given value is said to be upper bound for the zeros of the polynomial if all the…

Q: Find a forth degree polynomial that has the zeros 3, -2, i.

A: Explanation and Solution is given below....

Q: find the four zeroes of the polynomial z^4+4, one of them being z0=2^1/2e^ipi/4=1+i.then use those…

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Q: show that the polynomial p(x) = x^3 - 8x + 6 has exactly two roots on [0,3]

A: The given polynomial is p(x)=x3-8x+6. The roots of this polynomial are the values of x, where its…

Q: Show that the given values for a and b are lower and upper bounds for the real zeros of the…

A: Solution:-

Q: Which polynomial has 3i, -3i, and 3 (with multiplicity 2) as its roots? A x3 - 3x? + 9x + 27 B x* –…

A: Options  x3 - 3x2 +9x + 27  x4 – 6x3 + 54x - 81  x4 - 6x3 + 18x2 - 54x + 81  x4 - 6x3 + 12x2 - 18x…

Q: Consider a quadratic polynomial with a negativ main coefficient and a negative discriminant. Which…

A: Consider a quadratic polynomial with a negative main coefficient and a negative discriminant. Which…

Q: find a formula for the polynomial P(x) with degree 3 leading coefficient 1 zeros at -6, 4, and 7…

A:

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.