Find the values of `k` for which `5x^2-4x+2+k(4x^2-2x-1)=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 4x^(2)-2(k+1)x+(k+4)=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.

(i) Find the values of k for which the quadratic equation (3k+1)x^(2)+2(k+1)x+1=0 has real and equal roots. (ii) Find the value of k for which the equation x^(2)+k(2x+k-1)+2=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 (2k+1)x^(2)+2(k+3)x+(k+5)=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 (p) of k for which the equation x^(2) +5kx +16=0 has real and equal roots.

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 value of k for which the quadratic equation 3x^(2)+kx+3=0 has real and equal roots.