Question

find a third-degree polynomial equation with rational coefficients that has roots -4 and 6+i

x+^3-8x^2-11x+148=0
x+^3-8x^2-12x+37=0
x^3-12x^2+37x=0
x^3-8x^2-11x=0

Answer 1

First off, since a complex root of a real function will always have a conjugate, since 6 + i is a root, then 6-i must also be one.

Create factors from your roots:

(x - (-4)) (x - (6 + i)) (x - (6-i))

or

(x + 4)(x - (6+i))(x - (6-i))

Multiply the factors together to find your polynomial.

Answer 2

I would multiply the complex factors together first, then multiply the result by (x + 4) :)