Question

WILL MARK BRAINLIEST! Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4, -8, and 2 + 5i A.) f(x) = x^4 - 6x^3 - 20x^2 + 122x - 928 B.) f(x) = x^4 - 19x^2 + 244x - 928 C.) f(x) = x^4 - 6x^3 + 20x^2 - 122x + 928 D.) f(x) = f(x) = x^4 - 61x^2 + 244x - 928

Answer 1

Answer:

Step-by-step explanation:Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

4, -8, and 2 + 5i

A.) f(x) = x^4 - 6x^3 - 20x^2 + 122x - 928

B.) f(x) = x^4 - 19x^2 + 244x - 928

C.) f(x) = x^4 - 6x^3 + 20x^2 - 122x + 928

D.) f(x) = f(x) = x^4 - 61x^2 + 244x - 928

Answer 2

Answer:

B. f(x) = x^4 -19x^2 +244x -928

Step-by-step explanation:

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

4, -8, and 2 + 5i

A.) f(x) = x^4 - 6x^3 - 20x^2 + 122x - 928

B.) f(x) = x^4 - 19x^2 + 244x - 928

C.) f(x) = x^4 - 6x^3 + 20x^2 - 122x + 928

D.) f(x) = f(x) = x^4 - 61x^2 + 244x - 928

A polynomial function with real coefficients has complex roots in both conjugates, hence the minimum polynomial is of the 4th degree with roots

4, -8, 2 + 5i, 2 - 5i

A polynomial can be found by expanding the following factors:

P(x) = (x-4)(x+8)(x-2-5i)(x-2+5i)

= (x-4)(x+8)(x^2-4x+29)

= x^4 -19x^2 +244x -928