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Sum of roots of the equation x^2-2x^2sin...

Sum of roots of the equation `x^2-2x^2sin^2(pix)/2+1=0` is `0` (b) 2 (c) 1 (d) 3

A

0

B

2

C

1

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
`x^(4)-2x^(2) "sin"^(2) pi/2 x+1=0`
`rArr x^(4)+1=2x^(2) "sin"^(2) (pi x)/2`
`rArr x^(4)+1=2x^(2) (1-"cos"^(2) (pi x)/2)`
`rArr (x^(2)-1)^(2)+2x^(2) "cos"^(2) (pi x)/2=0`
`rArr (x^(2)-1)=0` and `2x^(2) "cos"^(2) (pi x)/2=0`
`rArr x= pm 1`
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