The equation `(2x^2)/(x-1)-(2x+7)/3+(4-6x)/(x-1)+1=0`has the roots

If f(x)=x^(3)+3x^(2)+6x+2sin x, then the equation (1)/(x-f(1))+(2)/(x-f(2))+(3)/(x-f(3))=0 has number of real roots of the equation?

If the equation (x^(2)+a|x|+a+1)(x^(2)+(a+1)|x|+a)=0 has no real root,then the range of values of a is

The equation x ^(4) -2x ^(3)-3x^2 + 4x -1=0 has four distinct real roots x _(1), x _(2), x _(3), x_(4) such that x _(1) lt x _(2) lt x _(3)lt x _(4) and product of two roots is unity, then : x _(1)x _(2) +x_(1)x_(3) + x_(2) x _(4) +x_(3) x _(4)=

The equation x^(4) -2x^(3) - 3x^(2) + 4x-1=0 has four distinct real roots x_1,x_2,x_3,x_4 such that x_1 lt x_2 lt x_3 lt x_4 and product of two roots is unity , then : x_1x_2+x_1x_3 + x_2x_4+x_3x_4 is equal to :

The equation x ^(4) -2x ^(3)-3x^2 + 4x -1=0 has four distinct real roots x _(1), x _(2), x _(3), x_(4) such that x _(1) lt x _(2) lt x _(3)lt x _(4) and product of two roots is unity, then : x _(1)x _(2) +x_(1)x_(3) + x_(2) x _(4) +x_(3) x _(4)=

Consider the equation x^(4)+x^(2)+1=0 .If x_(1),x_(2),x_(3),x_(4) are roots of this equation, then the value of x_(1)^(6)+x_(2)^(6)+x_(3)^(6)+x_(4)^(6) is equal to

If there is a multiple root of order 3 for the equation x^(4)-2x^(3)+2x1=0, then the other root is

If the roots of the equation 6x^3-11x^2+6x-1 =0 are in H.P., then the roots are

x_1 and x_3 are the roots of the equation Ax ^2 - 4x +1=0 and x_2 and x_4 =0 are the roots of the requation Bx^2 - 6x + 1=0 if x_1 , x_2 , x_3 ,x_4 form a H.P , then (A,B) =