Q. 104.7( 4 Votes )

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

Answer :

2x2 + 2px — 15 = 0


Put x = –5


2(–5)2 + 2p(–5) — 15 = 0


50 – 10p – 15 = 0


35 = 10p


p = 3.5


Equation p (x2 + x) + k = 0 has equal roots i.e. d = 0


p (x2 + x) + k = 0


p = 3.5


3.5 (x2 + x) + k = 0


3.5x2 + 3.5x + k = 0


d = b2 – 4ac


d = (3.5)2 – 4(3.5)(k)


d = 12.25 – 14k


Putting d = 0


Equation will be:


0 = 12.25 – 14k


14k = 12.25



k = 0.875


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