Let `a` and `b` be two distinct roots of the equation `x^3+3x^2-1=0` The equation which has `(ab)` as its root is

Number of distinct real roots of equation 3x^4+4x^3-12x^2+4=0

If a, b are the roots of the equation x^(2) - px +q = 0 , then find the equation which has a/b and b/a as its roots.

Let a and b be two distinct roots of a polynomial equation f(x) =0 Then there exist at least one root lying between a and b of the polynomial equation

Let a and b be two distinct roots of a polynomial equation f(x) =0 Then there exist at least one root lying between a and b of the polynomial equation

Let a,b and c be three distinct real roots of the cubic x ^(3) +2x ^(2)-4x-4=0. If the equation x ^(3) +qx ^(2)+rx+le =0 has roots 1/a, 1/b and 1/c, then the vlaue of (q+r+s) is equal to :

Let a,b and c be three distinct real roots of the cubic x ^(3) +2x ^(2)-4x-4=0. If the equation x ^(3) +qx ^(2)+rx+le =0 has roots 1/a, 1/b and 1/c, then the vlaue of (q+r+s) is equal to :

The number of distinct roots of the equation A"sin"^(3) x + B"cos"^(3)x +C = 0 no two of which differ by 2pi , is