Let's suppose-for the sake of a contradiction-that the three discriminants are $\leq 0 $ so: $ a_{i}^{2}\leq b_{i}\quad\forall i\in\{1,2,3\} $ and then $ (a_{1}a_{2}a_{3})^{2}\leq b_{1}b_{2}b_{3}=a_{1}a_{2}a_{3} $ wich implies that : $a_{1}a_{2}a_{3}\leq 1 $ wich is absurd.End$\blacksquare$