Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 29 of Exercise 10C
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29
Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
x2 + 5x – (a2 + a – 6) = 0
Given: x2 + 5x – (a2 + a – 6) = 0
Comparing with standard quadratic equation Ax2 + Bx + C = 0
A = 1, B = 5, C = – (a2 + a – 6)
Discriminant D = B2 – 4AC
= (5)2 – 4.1. – (a2 + a – 6)
= 25+ 4a2 + 4a – 24 = 4a2 + 4a + 1
= (2a + 1)2 > 0 Using a2 + 2ab + b2 = (a + b)2
Hence the roots of equation are real.
= (2a + 1)
Roots 
are given by
x = (a – 2) or x = – (a + 3)
Hence the roots of equation are (a – 2) or x = – (a + 3)
