Find a cubic polynomial in standard form with real coefficients, having the given zeros - 3 and 6 + 2i

p (x) = x³ - 9x² + 4x + 120

Step-by-step explanation:

complex zeros occur in conjugate pairs

6 + 2i is a zero, hence 6 - 2i is a zero

the factors are therefore (x + 3), (x - (6 + 2i)), (x - (6 - 2i)), hence

p (x) = (x + 3) (x - 6 - 2i) (x - 6 + 2i)

= (x + 3) ((x - 6) ² - 4i²)

= (x + 3) (x² - 12x + 36 + 4) ← i² = - 1

= (x + 3) (x² - 12x + 40)

= x³ - 9x² + 4x + 120 ← in standard form