Let $a,b,c$ be real with $a>0$. Then the roots of

are given by one of the following cases:

(i) if $b^{2}-4ac>0$, then there is a pair of distinct real roots

(ii) if $b^{2}-4ac=0$, then there is a double real root;

(iii) if $b^{2}-4ac<0$, then there is a pair of complex conjugate roots