Show that the roots of the equation x2 + px – q2 = 0 are real for all real values of p and q.
Given equation x2 + px – q2 = 0
a = 1 b = p x = – q2
Discriminant D = b2 – 4ac
= (p)2 – 4.1. – q2
= (p2 + 4q2) > 0
Thus the roots of equation are real.