use given info about a polynomial whose coefficients are real numbers to find the remaining zeros.

Question

Degree: 6 so I know there's at least 6
zeros:-5-isqrt7, 13 + 2ni, -5 - 3i
(where n is a real number)
any ideas??????

Answer 1

The idea is to remember that you're dealing with a polynomial with real coefficients. That means that any complex roots occur in conjugate pairs.

So, that means that the six roots are -5-isqrt7 -5+isqrt7
13+2ni 13-2ni
-5-3i -5+3i

Now you just multiply all the factors together to get the polynomial.