For m in R, let f(x) =x^(3)+3mx^(2)-3x-3...

For `m in R, let f(x) =x^(3)+3mx^(2)-3x-3m+2"has 3 real roots" x_(1),x_(2)and x_(3).` Also k denotes the value of m for which `(x_(1)^(2)+x_(2)^(2)+x_(3)^(2))` is minimum. Which of the following statements (s) is/are correct ?

f(x) has 3 roots real and distinct corresponding to m for which si `(x_(1)^(2)+x_(2)^(2)+x_(3)^(2))` minimum

The value of k lies in `(-1,1)`

The minimum value of `underset(i=1)overset(3)sumx_(1)^(2)`equal 6.

Number of roots of sin `sinx=k"in" [0,2pi]` equals 3.

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