Question

How do you write a polynomial function of least degree that has real coefficients, the following given zeros 2,-2,-6i and a leading coefficient of 1?

Answer 1

`f(x) = x^4+32x^2-144`

Explanation:

Since we want Real coefficients, any non-Real zeros must occur in Complex conjugate pairs.

So both `-6i` and `6i` are zeros and the simplest polynomial with these zeros is:

`f(x) = (x-2)(x+2)(x-6i)(x+6i)`

`= (x^2-2^2)(x^2-(6i)^2)`

`= (x^2-4)(x^2+36)`

`= x^4+32x^2-144`