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Question

If -5 is a root of the quadratic equation 2x2+px15=0 and the quadratic equation p(x2+x)+k=0 has equal roots, find the value of k.

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Solution

Given 5 is a root of the equation 2x2+px15=0.
Therefore,
2(5)25p15=0
5p=35
p=7

Putting p=7 in p(x2+x)+k=0, we get 7x2+7x+k=0

This equation will have equal roots, if
Discriminant = 0
494×7×k=0
k=4928
k=74

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