The real number k for which the equation `2x^(3) +3x +k=0` has two distinct real roots in [0,1]

Find the value of k for which the equation 3x^(2)-6x+k=0 has distinct and real root.

Find the values of k for which the equation x^2-4x+k=0 has distinct real roots.

The number of values of k for which the equation x^3-3x+k=0 has two distinct roots lying in the interval (0,1) is (a) three (b) two (c) infinitely many (d) zero

find the values k for which the quadratic equation 2x^2 + Kx +3=0 has two real equal roots

Statement-1: There is a value of k for which the equation x^(3) - 3x + k = 0 has a root between 0 and 1. Statement-2: Between any two real roots of a polynomial there is a root of its derivation.

The value of k for which the equation (k-2) x^(2) + 8x + k + 4 = 0 has both roots real, distinct and negative, is

The number of positive integral values of m , m le 16 for which the equation (x^(2) +x+1) ^(2) - (m-3)(x^(2) +x+1) +m=0, has 4 distinct real root is:

Find the value of a if x^3-3x+a=0 has three distinct real roots.

Find the value of a if x^3-3x+a=0 has three distinct real roots.