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±5i 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 + 5i)(x + 2 − 5i)
Now multiply the two complex polynomials.
(x + 2 + 5i)(x + 2 − 5i) = x2 + 4x + 29
Now multiply this equation by x + 1.
(x + 1)(x2 + 4x + 29)
x3 + 5x2 + 33x + 29