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Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
x2 – 2ax – (4b2 – a2) = 0
Given: x2 – 2ax – (4b2 – a2) = 0
Comparing with standard quadratic equation Ax2 + Bx + C = 0
A = 1, B = – 2a, C = – (4b2 – a2)
Discriminant D = B2 – 4AC
= (– 2a)2 – 4.1. – (4b2 – a2)
= 4a2 – 4a2 + 16 b2 = 16b2 > 0
Hence the roots of equation are real.
Roots are given by
x = (a + 2b) or x = (a – 2b)
Hence the roots of equation are (a + 2b) or (a – 2b)