Find value of `k` if equation `x^3-3x^2 + 2 = k` has i) 3 real roots ii)1 real root

Find the values of k for which the equation x^2+5k x+16=0 has no real roots.

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

Find the value of k for which equation 4x^(2)+8x-k=0 has real and equal roots.

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

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

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.

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.

Find the value of k for which the equation x^(2)+k(2x+k-1)+2=0 has real and equal roots.

Find the value of k for which the equation x^(2)+k(2x+k-1)+2=0 has real and equal roots.

(i) Find the values of k for which the quadratic equation (3k+1)x^(2)+2(k+1)x+1=0 has real and equal roots. (ii) Find the value of k for which the equation x^(2)+k(2x+k-1)+2=0 has real and equal roots.