Find the equation of the polynomial given the following information:

Question

x=3, x=i√7 and f(2)=33

I tried to solve it and got x^3-3x^2+7x-21, however it was wrong. Thank you in advance!

Answer 1

f(x) = a(x - 3)(x - √7 i)(x + √7 i) = a(x-3)(x² + 7)

Since f(2) = 33, we have a(-1)(11) = 33. So, a = -3

f(x) = -3(x-3)(x²+7) Multiply.