Question 0.1.21: Finding Zeros Using the Quadratic Formula Find the zeros o...

You probably won’t have much luck trying to factor this. However, from the quadratic formula, we have

x=\frac{-(-5) \pm \sqrt{(-5)^2-4 \cdot 1 \cdot(-12)}}{2 \cdot 1}=\frac{5 \pm \sqrt{25+48}}{2}=\frac{5 \pm \sqrt{73}}{2}.

So, the two solutions are given by x=\frac{5}{2}+\frac{\sqrt{73}}{2} \approx 6.772 \text { and } x=\frac{5}{2}-\frac{\sqrt{73}}{2} \approx-1.772. (No wonder you couldn’t factor the polynomial!)