Write a polynomial function of least degree with integral coefficients that has given zeros.

Question

-2, -4, 4, -3

 

A) f(x) = x^4 + 5x^3 - 10x^2 - 80x - 94

 

B) f(x) = x^4 + 7x^3 - 10x^2 - 80x - 96

 

C) f(x) = x^4 + 5x^3 - 10x^2 - 80x - 96

 

D) f(x) = x^4 + 5x^3 - 10x^2 - 84x - 96

Answer 1

Hello GOAT,

With the given zeros of -2, -4, 4, and -3, the factors are

x + 2, x + 4, x - 4, and x + 3.

 

So we can write

f(x) = (x + 2)(x + 4)(x - 4)(x + 3)

 

I am going to multiply the second and third factors together (since terms will drop out), and separately the first and last,

→f(x) = (x² + 5x + 6)(x² - 16)

→f(x) =x⁴ - 16x² + 5x³ - 80x + 6x² - 96

→f(x) =x⁴ + 5x³ - 10x² - 80x - 96.

 

So the answer is 'C'.

 

Thank you for posting the question.

Michael E.