If the equation
$$ax^2 +bx +c = 0$$
doesn't have $2$ distinct real roots and
then how could I prove that
$$f(x) = ax^2 + bx +c \geq 0.$$
I tried to prove $a>0$, since discriminant is already less than or equal to zero therefore if I prove $a>0$ then $f(x)$ will satisfy the above condition. But I'm not able to get $a>0$.