Find the polynomial function with roots of −2/5 and − 1 ± 2i and that passes through the point (−1,36)

Answer 1

x = -1 + or - 2i

x+1 = + or - 2i

x^2 +2x + 1 = -4

x^2+2x +5 = 0

x=-2/5

x+2/5 = 0

f(x) = a(x+2/5)(x^2 + 2x + 5)

f(-1) = 36 = a(-3/5)(4) = -12a/5

a = -(5/12)36 = -15

f(x) = -15(x+2/5)(x^2+2x+5)= (-15x-6)(x^2+2x+5)

f(x) = -15x^3 -36x^2 -87x -30