Q. 114.0( 12 Votes )

If – 5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p (x2 + x) + k = 0 has equal roots, find the value of k.

Answer :

Given that – 5 is a root of the quadratic equation 2x2 + px – 15 = 0

2(– 5)2 – 5p – 15 = 0


5p = 35


p = 7


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


px2 + px + k = 0


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


a = p b = p c = k


Given that the roots of equation are equal


Thus D = 0


Discriminant D = b2 – 4ac = 0


[p]2 – 4.p.k = 0


72 – 28k = 0


49 – 28k = 0



The value of k is for which roots of the quadratic equation are equal.


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