Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 33 of Exercise 10C
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33
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)
