build a polynomial with real coefficients given the degree and zeros.

Question

degree of 4 and zeros: 4, multiplicity 2; 6i

Answer 1

Since 6i is a zero of f(x), so is -6i..

f(x) = (x-4)²(x-6i)(x-(-6i))

= (x-4)²(x-6i)(x+6i)

= (x² - 8x + 16)(x² + 36)

= x⁴ + 36x² - 8x³ - 288x + 16x² + 576

= x⁴ - 8x³ + 52x² - 288x + 576