Find the roots of the equation when the sum $2$ and product is $-8$.

#### Solution

Let $\alpha, \beta$ be the roots of quadratic.
So, quadratic equation will be like;
$a\left( {x - \alpha } \right)\left( {x - \beta } \right) = 0$
$\Rightarrow a\left( {{x^2} - \left( {\alpha + \beta } \right)x + \alpha .\beta } \right) = 0$
$a\left( {{x^2} - \left( {sum\,of\,roots} \right).x + \left( {products\,of\,roots} \right).x} \right) = 0$
${x^2} + 2x - 8 = 0$
$x^2+4x-2x-8=0$
$x(x+4)-2(x+4)$
$(x+4)(x-2)$
So, the roots are $-4$ & $2$