Question

for what value of k (4-k)x2+(2 k+4)x+(8k+1)=0

Answer 1

The given quadratic will be a perfect square if it has two real and equal roots. To have two real and equal roots the discriminant must be zero.
i.e., b²-4ac=0
or, (2k+4)²-4(4-k)(8k+1)=0
or, 4k²+16k+16-4(32k-8k²+4-k)=0
o², 4k²+16k+16-128k+32k²-16+4k=0
or, 36k²-108k=0
or, 36k(k-3)=0
either 36k=0
or, k=0
or, k-3=0
or, k=3
∴, k=0,3 Ans.

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