Question

Find the sum and product of the roots. 2x^2 + 6x - 8 = 0

Answer 1

Suppose you can factorize:

$ax^2+bx+c=a(x-r_1)(x-r_2)$

Then by expanding the right side, you have

$ax^2+bx+c=a(x^2-(r_1+r_2)x+r_1r_2)=ax^2-a(r_1+r_2)x+ar_1r_2$

which means in this case, you have to have

$\begin{cases}6=-2(r_1+r_2)\\-8=2r_1r_2\end{cases}\implies\begin{cases}r_1+r_2=-3\\r_1r_2=-4\end{cases}$