Q. 44.7( 6 Votes )

For what values of k are the roots of the quadratic equation 3x2 + 2kx + 27 = 0 real and equal?

Answer :

Given: 3x2 + 2kx + 27 = 0

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


a = 3 b = 2k c = 27


Given that the roots of equation are real and equal


Thus D = 0


Discriminant D = b2 – 4ac = 0


(2k)2 – 4.3.27 = 0


4k2 – 324 = 0


4k2 = 324


k2 = 81 taking square root on both sides


k = 9 or k = – 9


The values of k are 9, – 9 for which roots of the quadratic equation are real and equal.


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