Question

Given that three -3 I zero, find the remaining zero of the following polynomial function use the CONGUGATE root theorem if applicable write the exact answer do not round separate multiple answers with a comma

Answer 1

Given:

$f(x)=x^4+6x^3+22x^2+24x+576$

and the one solution is 3-3i.

Find: remaining zeroes

Explanation:

$f(x)=[x-(3-3i)][x-(3+3i)]Q(x)$

where Q(x) is second order polynomial.

then

$Q(x)=x^2+12x+32$$x^2+12x+32=(x+4)(x+8)$

so the solution of the equation is 3+3i,3-3i, -4 and -8