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Question

Let S be the sum of all x in the interval [0,2π] such that 3cot2x+8cotx+3=0, then the value of Sπ is

A
3
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B
4
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C
5
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D
6
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Solution

The correct option is C 5
3cot2x+8cotx+3=0
cotx=4±73
Both roots are negative.
π2<x1,x2<π or 3π2<x1,x2<2π
π<x1+x2<2π or 3π<x1+x2<4π

Product of roots =cotx1cotx2=1
cotx1cot(3π2x1)=1
x1+x2=3π2
Similarly, x1+x2=7π2

S = 3π2+7π2=5π

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