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The number of distinct real roots of the...

The number of distinct real roots of the equation `sin pi x=x^(2)-x+(5)/(4)` is

A

0

B

1

C

2

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
`sin pi x = x^(2)-x + (5)/(4)`
`rArr sin pi x = (x-1//2)^(2)+1`
`rArr sin pi x le 1` and `x^(2)-x + (5)/(4) ge 1`
`therefore sin pi x = 1` and `x = (1)/(2)`
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