Question

Which of the following is a polynomial with roots 4, 2i, and −2i?

f(x) = x3 − 4x2 + 8x − 4
f(x) = x3 − 8x2 + 16x − 4
f(x) = x3 − 4x2 + 4x − 16
f(x) = x3 − 4x2 + 8x − 16

Answer 1

if the roots are r1,r2,r3, the facotred polynomail looksl ike this
f(x)=(x-r1)(x-r2)(x-r3)

given
roots 4,2i and -2i

f(x)=(x-4)(x-2i)(x-(-2i))
f(x)=(x-4)(x-2i)(x+2i)
expand
f(x)=x³-4x²+4x-16
3rd option