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

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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