Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

x^{2} – 4x – 1 = 0

Given: x^{2} – 4x – 1 = 0

Comparing with standard quadratic equation ax^{2} + bx + c = 0

a = 1, b = – 4, c = – 1

Discriminant D = b^{2} – 4ac

= (– 4)^{2} – 4.1. – 1

= 16 + 4 = 20 > 0

Hence the roots of equation are real.

Roots are given by

Hence the roots of equation are

2