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Question

For what value of k,(4k)x2+2(k+2)x+(8k+1) is a perfect square i.e. has equal roots

A
k = 3
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B
k = 0
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C
does not exist
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D
Both A & B
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Solution

The correct option is D Both A & B
perfect square = equal roots =Δ=0
(2(k+2))24(4k)(8k+1)=0
4(k2+4+4k)4(32k+48k2k)=0
k2+4+4k32k4+8k2+k=0
9k227k=0
k23k=0
k(k3)=0
k=0 or k=3

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