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

The least value of k which makes the roots of the equation x^(2) + 5x + k = 0 imaginary is

The value of k for which the sum of the squares of the roots of 2x^(2)-2(k-2)x-k=0 is least is

If the roots of the quadratic equation 2x^(2)+8x+k=0 are equal, find the value of k .

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

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