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Question

The sum of value(s) of k for which the equation ((log5k)2+(log5k)2)x2(22k342k+64)x+(k2+7k60)=0 possesses more than two roots, is

A
5
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B
7
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C
10
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D
12
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Solution

The correct option is A 5
((log5k)2+log5k2)x2(22k342k+64)x+(k2+7k60)=0
For the equation to have more than 2 roots, it should be an identity, so
(log5k)2+log5k2=0(log5k+2)(log5k1)=0log5k=2,1k=125,5 (1)

22k342k+64=0(2k32)(2k2)=02k=2,32k=1,5 (2)

k2+7k60=0(k+12)(k5)=0k=12,5 (3)

From equations (1),(2) and (3),
k=5
Hence, sum of all values of k is 5.

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