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

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

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:

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

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(kcos^-1p) , then the value of n+1/k is :