Let 'k' be a real number. The minimum number of distinct real roots possible of the equation `(3x^2+kx+3)(x^2+kx-1)=0` is

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

The number of distinct real roots of the equation tan ( 2 pi x)/( x^(2) + x + 1) = - sqrt(3) is

The number of distinct real roots of the equation 3x^(4)+4x^(3)-12x^(2)+4=0 is ___________.

Let 'a' be a real number.Number of real roots of the equation (x^(2)+ax+1)(3x^(2)+ax-3)=0, is-

If f(x)=x^(3)-3x+1, then the number of distinct real roots of the equation f(f(x))=0 is

The number of distinct real root of x^3-3x+1=0 in (1,2) is

Let the roots of the equation 24 x ^(3) -14x ^(2) + kx +3=0 form a geometric sequence of real numbers. If absolute value of k lies between the roots of the equation x ^(2)+alpha ^(2) x -122=0, then the largest integral value of alpha is :

Let the roots of the equation 24 x ^(3) -14x ^(2) + kx +3=0 form a geometric sequence of real numbers. If absolute value of k lies between the roots of the equation x ^(2)+alpha ^(2) x -122=0, then the largest integral value of alpha is :

Write True or False The roots of the equation x^2+kx+1=0 will be real if k^2<4 .