Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 15 of Exercise 10A
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15
Solve each of the following quadratic equations:
3x2 - 2x - 1 = 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 = 3; b = -2; c = -1
= 3. - 1 = - 3
And either of their sum or difference = b
= - 2
Thus the two terms are - 3 and 1
Difference = - 3 + 1 = - 2
Product = - 3.1 = - 3
3x(x-1) + 1(x-1) = 0
(x-1)(3x + 1) = 0
(x-1) = 0 or (3x + 1) = 0
x = 1 or x = (-1)/3
Roots of equation are 1, (-1)/3
