How can I find the answer

Question

Suppose that a polynomial function of degree 4 with radiation coefficient has the given numbers as zeros.find the other zero.

6i,0,-1

Answer 1

0, -1, 6i, -6i are 4 roots

imaginary roots come in conjugate pairs. if 6i is a root so is -6i

corresponding factor multiplied together are

x(x+1)(x+6i)(x-6i)

= (x^2+x)(x^2+36)

= x^4 + x^3 +36x^2 +36x = the 4th degree polynomial with the given roots

Answer 2

Hello Josh,

You're told it's a degree 4 polynomial and you're given 3 zeros: 6i, 0 and -1.

The key is remembering that complex zeros (meaning zeros that have the letter i in them) ALWAYS come in twos: the complex zero and its conjugate.

Among the 3 zeros given, one of them is complex: 6i.

The 4th zero is the conjugate of 6i, which is -6i.

Therefore, the answer to "find the other zero" is -6i