Show that the roots of the equation x2+px−q2=0 are real for all real values of p and q
Given equation is:
x2 + px – q2 = 0
The discriminant of the given equation is given by
D = p2 – 4 × (1) × (–q2)
= p2 + 4q2
Clearly, D = p2 + 4q2 > 0 for all p, q ∈ R.
Hence, the given equation has real roots.