Chapter 7 - Polynomial Equations and Factoring - 7.4 - Solving Polynomial Equations in Factored Form - Exercises - Page 381: 17

The roots are $r=4$ and $r=-8$.

Given: $(r-4)^{2}(r+8)=0$ $\implies (r-4)(r-4)(r+8)=0$ Using zero-product property, we have $r-4=0$ or $r-4=0$ or $r+8=0$. Solving for $r$, we get $r=4$ or $r=-8$. The roots are $r=4$ and $r=-8$.