CPM Homework Help : A2C Problem 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, $−2±5i$ and one real zero, −1. What could his original function have been?

Step 1:

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

$\left(x + 1\right)\left(x + 2 + 5i\right)\left(x + 2 − 5i\right)$

Step 2:

Now multiply the two complex polynomials.

$\left(x + 2 + 5i\right)\left(x + 2 − 5i\right) = x^{2} + 4x + 29$

Step 3:

Now multiply this equation by $x + 1$ .

$\left(x + 1\right)\left(x^{2} + 4x + 29\right)$

Answer:

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