### Home > A2C > Chapter 9 > Lesson 9.3.2 > Problem 9-148

9-148.

Spud has done it again. He's lost another polynomial function. This one was a cubic, written in standard form. He knows that there were two complex zeros, −2±5*i* and one real zero, −1. What could his original function have been? Homework Help ✎

Use the three roots to find the individual polynomials that make up the cubic equation.

(*x* + 1)(*x* + 2 + 5*i*)(*x* + 2 − 5*i*)

Now multiply the two complex polynomials.

(*x* + 2 + 5*i*)(*x* + 2 − 5*i*) = *x*^{2} + 4*x* + 29

Now multiply this equation by *x* + 1.

(*x* + 1)(*x*^{2} + 4*x* + 29)

*x*^{3} + 5*x*^{2} + 33*x* + 29