find polynomial function

Question

Find the polynomial function f with real coefficients that has the given degree, zeros, and solution point. Degree:3, zeroes: -7, 1+sq. root of 3i, Solution points f(-2)=60

Answer 1

(x+7) [ (x-1) - sqrt(3i)] [ (x-1) + sqrt(3i)] =

(x+7) [ (x-1)^2 + 9 ] =

(x+7) [ x^2 - 2x + 1 + 9 ] =

(x+7) ( x^2 - 2x + 10) =

x^3 - 2x^2 + 10x

7x^2 - 14x + 70 =

x^3 + 5x^2 - 4x + 70 = f(x)

k * f(-2) = 60

k ((-2)^3 + 5(-2)^2 - 4(-2) + 70) = 60

k ( -8 + 20 + 8 + 70) = 60

k( 90) = 60

k = 60/90 = 2/3