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Question

If 5 is one of the zeroes of 2x2+px15. Quadratic polynomial p(x2+x)+k has both the zeros equal to each other. Then find k.

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Solution

Given, 2x2+px15=0

As 5 is one of the zeroes of the above equation.

2(5)2+p(5)15=0

505p15=0

5p=35

p=7

Putting the value of p in the given polynomial we get

7x2+7x+k

It is given that it has both the zeros equal to each other

D=0b24ac=0

(7)24(7)(k)=0

28k=49

k=74

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