1.

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

Answer»

x2 + px – q2 = 0

Compare given equation with the general form of quadratic equation, which is ax2 + bx + c = 0

a = 1, b = p, c = -q2

Using discriminant formula:

D = b2 – 4ac

= (p)2 – 4 x 1 x (-q2)

= p2 + 4 q2 > 0

Hence roots are real for all real values of p and q.



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