Question

Which of the following is a polynomial with roots 5, 4i, and -4i?

Answer 1

The correct answer is x^3 - 5x^2 + 16x - 80.

In order to find this, we work backwards. Start by creating true statements for each of the roots.

x = 5

x = +/-4i

Now we can solve all of these until they are statements that equal 0.

x = 5 ----> Subtract 5 from both sides

x - 5 = 0

x = +/-4i ------> Square both sides

x^2 = -16 ---> Add 16 to both sides.

x^2 + 16 = 0

Now we can use the two statements that we have and multiply them to get the polynomial.

(x - 5)(x^2 + 16)

x^3 - 5x^2 + 16x - 80