Determine the polynomial of least degree given the zeros 3-i and -2.

Question

please answer and show steps. im desperate to pass this class.if you want to help then tell me

Answer 1

Assuming that the polynomial has real coefficients, complex roots occur in conjugate pairs. So, since 3 - i is a root, so is 3 + i.

A polynomial with the given roots is (x + 2)[x - (3-i)][x - (3+i)]

= (x + 2){(x-3) + i][(x-3) - i] = (x + 2)[(x-3)² - i²]

= (x + 2)(x² - 6x + 10) = x³ - 6x² + 10x + 2x² - 12x + 20 = x³ - 4x² - 2x + 20