Solve each of the following quadratic equations:

48x^{2} - 13x - 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 = 48; b = -13 ;c = -1

= 48× - 1 = - 48

And either of their sum or difference = b

= - 13

Thus the two terms are - 16 and 3

Difference = - 16 + 3 = - 13

Product = - 16.3 = - 48

16x(3x-1) + 1(3x-1) = 0

(16x + 1)(3x-1) = 0

(16x + 1) = 0 or (3x-1) = 0

x = (-1)/6 or x = 1/3

Roots of equation are

19