`|||x-1|-3|-a|=k, a in N`, has eight distinct real roots for some K, then number of such values of 'a' is

Let f(x)=x^(3)-12x be function such that the equation |f(|x|)|=n(n in N) has exactly 6 distinct real roots then number of possible values of n are

If the equation sin ^(2) x - k sin x - 3 = 0 has exactly two distinct real roots in [0, pi] , then find the values of k .

if the equation x^(2)-x=k-k^(2) (k in R) has one positive and one negative real roots, then number of possible integral values of "k" is

If x^2 + kx + k =0 has two distinct real solutions, then the value of k will satisfy:

If the equation x^(2)+4x+k=0 has real and distinct roots, then find the value of 'k'.

The equation k+x^(3)e^(x+3)=0 has 2 distinct real roots & k is a prime natural number, then the possible value of k is/are

If the equation x ^(4)+kx ^(2) +k=0 has exactly two distinct real roots, then the smallest integral value of |k| is:

Consider the equation x^(4)+4x^(3)-8x^(2)+K=0. Answer the following (1) The above equation has all imaginary roots then the range of k is (2) The above equation has 3 -distinct real roots if the range of k is (3) the above equation has 2 real roots and 2 imaginary roots if the range of k is

Show that the equation x^(2)+ax-4=0 has real and distinct roots for all real values of a .

For -1<=p<=1, the equation 4x^(3)-3x-p=0 has 'n' distinct real roots equation in the interval [(1)/(2),1] and one its root is cos(k cos^(-1)p), then the value of n+(1)/(k) is :