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Which of the following statement(s) is/a...

Which of the following statement(s) is/are correct ?

A

The number of quadratic equations having real roots which remain unchanged even after squaring their roots is 3.

B

The number of solutions of the equation `tan 2 theta+ tan 3 theta =0,` in the interval `[0, pi]` is equal to 6.

C

For `x _(1), x _(2), x _(3) gt 0` the minimum values of `(2x _(1))/(x _(2))+ (128 x _(3)^(2))/(x _(2)^(2)) + (x _(2)^(2))/(4x _(1)x _(3)^(2)) ` equals 24.

D

The locus of the mid-points of chords of the circel `x ^(2) + y^(2) -2x -6y -1=0,` which are passing through origin is `x ^(2) +y^(2) -x-3y =0.`

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