Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 42 of Exercise 10A
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Solve each of the following quadratic equations:
x2 + 5x - (a2 + a - 6) = 0
x2 + 5x - (a2 + a - 6) = 0
Using the splitting middle term - the middle term of the general equation 
is divided in two such values that:
Product = a.c
For the given equation a = 1; b = 5; c = - (a2 + a - 6)
= 1. - (a2 + a - 6)
= - (a2 + a - 6)
And either of their sum or difference = b
= 5
Thus the two terms are (a + 3) and - (a - 2)
Difference = a + 3 –a + 2
= 5
Product = (a + 3). - (a - 2)
= - [(a + 3)(a - 2)]
= - (a2 + a - 6)
x2 + 5x - (a2 + a - 6) = 0
⇒ x 2 + (a + 3)x - (a - 2)x - (a + 3)(a - 2) = 0
⇒ x[x + (a + 3)] - (a - 2) [x + (a + 3)] = 0
⇒ [x + (a + 3)] [x - (a - 2)] = 0
⇒ [x + (a + 3)] = 0 or [x - (a - 2)] = 0
⇒ x = - (a + 3) or x = (a - 2)
Hence the roots of given equation are - (a + 3) or (a - 2)
