Q. 264.5( 4 Votes )

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

x2 – 2ax + (a2 – b2) = 0

Answer :

Given: x2 – 2ax + (a2 – b2) = 0

Comparing with standard quadratic equation Ax2 + Bx + C = 0

A = 1, B = – 2a, C = a2 – b2

Discriminant D = B2 – 4AC

= (– 2a)2 – 4.1.(a2 – b2)

= 4a2 – 4a2 + 4 b2 = 4 b2 > 0

Hence the roots of equation are real.

Roots are given by

x = (a + b) or x = (a – b)

Hence the roots of equation are (a + b) or (a – b)

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