Question

why if alpha and bita are the roots of quadratic equation then ( x-alpha) (x- bita) =0

Answer 1

Let a quadratic equation be

$ax^{2} +bx+c=0$  ,where a,b and c are constants and whose roots are $\alpha and \beta$

This means that the solution can be either α or β i.e the LHS will be equal to RHS if and only if x's value equals either α or β

So,if x=α then x-α=0 therefore (x-α)(x-β)=0

else if x=β then x-β=0 therefore (x-α)(x-β)=0

Hope this helps : )