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Question

The number of values of x in [0,2π] satisfying the equation 3cos2x10cosx+7=0 is

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is D 4
Given, 3cos2x10cosx+7=0
3(2cos2x1)10cosx+7=0
6cos2x10cosx+4=0
3cos2x5cosx+2=0
(3cosx2)(cosx1)=0
cosx=1orcosx=23
x=0,2πorx=cos123,2πcos123
Hence, four values exit, when x[0,2π].

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