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The equation x^2 - 2 = [sin x], where [....

The equation `x^2 - 2 = [sin x], where [.]` denotes the greatest integer function, has

A

infinity many roots

B

exactly one integer root

C

exactly one irrational root

D

exactly two roots

Text Solution

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The correct Answer is:
B, C, D
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Knowledge Check

  • Number of solutions of the equation x^(2)-2=[sinx] , where [.] denotes the greatest integer function, is

    A
    3
    B
    4
    C
    2
    D
    1

  • The function f(x)={x} sin (pi[x]) , where [.] denotes the greatest integer function and {.} is the fractional part function, is discontinuous at

    A
    all x
    B
    all integer points
    C
    no x
    D
    x which is not an integer

  • The function f(x) = {x} sin (pi [x]) , where [.] denotes the greatest integer function and {.} is the fraction part function , is discontinuous at

    A
    all x
    B
    all integer points
    C
    no x
    D
    x which Is not an interger

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