Find the number of integral values of k for which `x^2+2(k+1)x+(k^2+4k-2)=0` has equal roots.

Find the values of k for which 4x^(2)-2(k+1)x+(k+4)=0 has real and equal roots.

Find the values of k for which (2k+1)x^(2)+2(k+3)x+(k+5)=0 has real and equal roots.

Find the value of k for which x^(2) + k(4x + k - 1) + 2 = 0 has real and equal roots.

Find the values of k for which 5x^(2)-4x+2+k(4x^(2)-2x-1)=0 has real and equal roots.

Find the values of k for which (4-k)x^(2)+(2k+4)x+(8k+1)=0 has real and equal roots.

Find the values of k for which (k+1)x^(2)-2(3k+1)x+8k+1=0 has real and equal roots.

Find the value of k for which the equation x^(2)+k(2x+k-1)+2=0 has real and equal roots.

What is the least integral value of k for which the equation x^(2) - 2(k-1)x + (2k+1)=0 has both the roots positive ?

For what values of k, the equation x^2+2(k-4) x + 2k=0 has equal roots?

The number of integral values of k for which the inequality x^(2)-2(4k-1)x+15k^(2)-2k-7 ge0 hold for x in R are _____________