Find the values of `a` for which the roots of the equation `x^2+a^2=8x+6a` are real.

Find the values of a for which all the roots of the equation x^4-4x^3-8x^2+a=0 are real.

Find the value of 'k' for which the roots of the equation (5k-6)x^(2) + 2kx+1=0 are real and equal .

Find the value of 'k' for which the roots of the following equations are real and equal kx^(2)+(6k+2)x+16=0

Find the value of 'k' for which the roots of the following equations are real and equal (5k-6)x^(2)+2kx+1=0

Find the values of P for which the difference between the roots of the equation x^(2) + px + 8 = 0 is 2.

The roots of the equation x^(2) - 8x + 12 = 0 are ………… .

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