Ernie and Lisa were trying to find the roots of a quadratic function g(x) by solving g(x) = 0. Ernie's answer was $- 3 \pm \sqrt { \frac { 17 } { 2 } }$. Lisa's answer was $\frac { - 6 \pm \sqrt { 34 } } { 2 }$ Without using a calculator, show that both answers are equivalent and figure out what their original quadratic function g(x) might have been.