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

x² – (2b – 1)x + (b² – b – 20) = 0

Given: x² – (2b – 1)x + (b² – b – 20) = 0

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

A = 1, B = – (2b – 1), C = (b² – b – 20)

Discriminant D = B² – 4AC

= [ – (2b – 1)²] – 4.1. (b² – b – 20) Using a² – 2ab + b² = (a – b)²

= 4b² – 4b + 1 – 4b² + 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)