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 $$-4$$ & $$2$$