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The number of distinct real roots of the...

The number of distinct real roots of the equation `tan(2pix)/(x^2+x+1)=-sqrt(3)` is 4 (b) 5 (c) 6 (d) none of these

A

4

B

5

C

6

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have `"tan" (2 pi x)/(x^(2) +x+1) = -sqrt(3), x ne 0`
`rArr (2 pi x)/(x^(2) + x+1) = n pi - pi/3, n in Z`
`rArr x+1/x=(7-3n)/(3n-1)`
`rArr n=0, pm 1 ("as " L.H.S. le -2 or ge 2)`
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