Question

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

x² - 4x - 1 = 0

Answer 1

Given

x² - 4x - 1 = 0

On comparing it with ax² + bx + c = 0, we get: 

a = 1,

b = - 4

and c = -1

Discriminant D is given by:

D = (b² - 4ac)

= (-4)² - 4 x 1 x (-1)

= 16 + 4

= 20

= 20>0

Hence, the roots of the equation are real. 

Roots α and β are given by:

Thus, the roots of the equation are (2 + √5) and (2 - √5)