Q. 24.3( 3 Votes )

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

x2 – 4x – 1 = 0

Answer :

Given: x2 – 4x – 1 = 0

Comparing with standard quadratic equation ax2 + bx + c = 0


a = 1, b = – 4, c = – 1


Discriminant D = b2 – 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


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