Question

Find the polynomial of least degree in standard form with the given roots: x = 2, 3i

Answer 1

Answer:

x^3 - 2x^2 + 9x - 18.

Step-by-step explanation:

The complex roots occur in conjugate pairs so there are 3 roots 2, 3i and -3i.

So we have:

P(x) = (x - 2)(x - 3i)(x + 3i)

= (x - 2)(x^2 - 9i^2)

= (x - 2)(x^2 - 9*-1)

= (x - 2)(x^2 + 9)

= x^3 + 9x - 2x^2 - 18

= x^3 - 2x^2 + 9x - 18.