Question 745890
complex roots of polynomials with real always come in conjugate pairs so if 5i is a root, then so is -5i.

so the general polynomial is...


{{{p=Q(x)(x-4)(x-5i)(x+5i)}}}

but the principal polynomial is


{{{p=(x-4)(x-5i)(x+5i)}}}


{{{(x-4)(x^2+25)}}}


{{{x(x^2+25)-4(x^2+25)}}}


{{{x^3+25x-4x^2-100)}}}


{{{x^3-4x^2+25x-100)}}}