Question

Write the cubic polynomial in standard form that has the given roots,-2, 2i and -2i

Answer 1

The factor for x=-2 would be (x+2)

The factor for x=2i and x=-2i is (x^2+4)

The product of the factors would be:

(x+2)*(x^2+4)

x^3+4x + 2x^2 + 8 (Multiplying factors)

x^3 + 2x^2 + 4x + 8 (Organizing)

The answer is: x^3 + 2x^2 + 4x + 8