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Question

If the roots of the equation 4x2+5k=(5k+1)x differ by unity, then the negative value of k is

A
3
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B
15
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C
35
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D
Noneofthese
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Solution

The correct option is C 15
Let the roots of the equation
4x2(5k+1)x+5x=0 be α and α+1
α+α+1=5k+14α=5k38 and α(α+1)=5k4
(5k3)(5k3+8)8×8=5k4
(5k3)(5k+5)=80k
(5k3)(k+1)=16k
5k214k3=0
(k3)(5k+1)=0
k=3,15
Hence, negative value of k is 15

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