consider the following statement `S_(1)` : If `x` is in radian and `2sin^(2)x + 3sin x -2 gt 0 and x^(2) -x-2 lt 0 " then " x in ( pi/6, 2)` `S_(2) : "If" x in ( 0, pi/2) and x cancelin { -1,0} ` then the expression ` sqrt(x^(2)+x) + (tan^(2)alpha)/(sqrt(x^(2)+x))` is always greater than or equal to ` 2tan alpha` `S_(3)` : If a,b,c are the sides of a triangle ABC such that ` x^(2) -2 (a +b+c) x + 3lambda(ab+bc+ca)= 0 " then " lambda lt 4/3 ` ` S_(4) : " If the equations " x^(3) + 3px^(2) +3qx + r=0 and x^(2) +2px +q =0` have a common root then ` 4(p^(2) -q)(q^(2) -pr) = ( pq -r)^(2)` The correct combination of true statements is

Options

A. `S_(1)` only
B. `S_(2)` only
C. `S_(3)` only
D. `S_(1),S_(2),S_(3),S_(4)`

Answer

D