Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
x2 – 2ax + (a2 – b2) = 0
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)