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

x^{2} – (2b – 1)x + (b^{2} – b – 20) = 0

Given: x^{2} – (2b – 1)x + (b^{2} – b – 20) = 0

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

A = 1, B = – (2b – 1), C = (b^{2} – b – 20)

Discriminant D = B^{2} – 4AC

= [ – (2b – 1)^{2}] – 4.1. (b^{2} – b – 20) Using a^{2} – 2ab + b^{2} = (a – b)^{2}

= 4b^{2} – 4b + 1 – 4b^{2} + 4b + 80 = 81 > 0

Hence the roots of equation are real.

Roots are given by

x = (b + 4) or x = (b – 5)

Hence the roots of equation are (b + 4) or (b – 5)

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