The smallest value of k, for which both the roots of the equation, `x^2-8kx + 16(k^2-k + 1)=0` are real, distinct and have values at least 4, is

The smallest value of k for which both the roots of the equation x^(2)-8kx+16(k^(2)-k+1)=0 are real distinct and have value atleast 4, is

The number of values (s) of k , for which both the roots of the equation x^(2) -6kx + 9(k^(2)-k+1)=0 are real, distinct and have values atmost 3 is ________

If lambda is a smallest possible integral value of k, for which roots of the equation x^(2)-8kx+16(k^(2)-k+1)=0 are real and distinct and A=[[lambda,lambda+1],[lambda+1,lambda]] then ||(1/5 A^(-1))||=

If the roots of the equation kx^2 + (k- 1) x - 1 = 0 are equal then find the value of k.

For what values of k , the roots of the equation x^(2) + 4x + k = 0 are real ?

If the roots of the quadratic equation x^(2)-2kx+2k^(2)-4=0 are real,then the range of the values of k is

Find the nonzero value of k for which the roots of the quadratic equation 9x^(2)-3kx+k=0 are real and equal.

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