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Question

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

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Solution

Given,
p(x2+x)+k=0
has equal roots
so,b2=4ac
px2+px+k=0
(p)2=4(p)(k)
p=0,orp=4k
and given -5 is root of 2x2+px15=0
put x=5
2(5)2+(5)p15=0
505p15=0
p=7
7=4k
k=7/4

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