Q. 124.1( 15 Votes )

If 3 is a root of the quadratic equation x2 – x + k = 0, find the value of p so that the roots of the equation x2 + k (2x + k + 2) + p = 0 are equal.

Answer :

Given 3 is a root of the quadratic equation x2 – x + k = 0

(3)2 – 3 + k = 0


k + 6 = 0


k = – 6


Given equation is x2 + k (2x + k + 2) + p = 0


x2 + 2kx + (k2 + 2k + p) = 0


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


a = 1 b = 2k c = k2 + 2k + p


Given that the roots of equation are equal


Thus D = 0


Discriminant D = b2 – 4ac = 0


(2k)2 – 4.1. (k2 + 2k + p) = 0


4k2 – 4k2 – 8k – 4p = 0


– 8k – 4p = 0


4p = – 8k


p = – 2k


p = – 2. – 6 = 12


p = 12


The value of p is – 12 for which roots of the quadratic equation are equal.


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