Question

Show that the roots of the equation x² + px – q² = 0 are real for all real values of p and q.

Answer 1

Given: 

x² + px – q² = 0

Here,

a = 1, b = p and c = –q² 

Discriminant D is given by: 

D = (b² – 4ac)

= p² – 4 × 1 × (–q²) 

= (p² + 4q²) > 0

D > 0 for all real values of p and q.

Thus, the roots of the equation are real.