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

x^{2} – 2ax – (4b^{2} – a^{2}) = 0

Given: x^{2} – 2ax – (4b^{2} – a^{2}) = 0

Comparing with standard quadratic equation Ax^{2} + Bx + C = 0

A = 1, B = – 2a, C = – (4b^{2} – a^{2})

Discriminant D = B^{2} – 4AC

= (– 2a)^{2} – 4.1. – (4b^{2} – a^{2})

= 4a^{2} – 4a^{2} + 16 b^{2} = 16b^{2} > 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)

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