Find a formula for the polynomial P ( x ) with degree 3 real coefficients zeros at x = − 5 + 4 i and x = − 6 y -intercept at ( 0 , 492 )

Answer 1

The polynomial is a(x - (-5 + 4i))(x - (-5 - 4i))(x - -6) = a(x^2 - 10x + 41)(x+6)

f(0) = a(41)(6) = 246a

246a = 492

a = 2

f(x) = 2(x² - 10x + 41)(x + 6) = 2(x³-4x² - 19x + 246) = 2x³ - 8x² - 38x + 492