Find the roots of the quadratic equation 2x^{2} - x - 6 = 0.

Given: 2x^{2} - x - 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 = 2 b = - 1 c = - 6

= 2. - 6 = - 12

And either of their sum or difference = b

= - 1

Thus the two terms are - 4 and 3

Sum = - 4 + 3 = - 1

Product = - 4.3 = - 12

2x^{2} - 4x + 3x - 6 = 0

2x(x - 2) + 3(x - 2) = 0

(x - 2) (2x + 3) = 0

x = 2 or x = - 3/2

Hence the roots of the given equation x = 2 or x =

36