Find the value of k for which the equation `3x^(2)-6x+k=0` has distinct and real root.

Find the values of k for which the equation x^2-4x+k=0 has distinct real roots.

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

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

Find the values of k for which the equation x^2+5k x+16=0 has no real roots.

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

Find the value of k for which the equation 9x^2-24 x+k=0 has equal roots. Also, find the roots.

Find the value of k for which the equation 2k x^2-40 x+25=0 has equal roots. Also, find the roots.

Find the least positive value of k for which the equation x^2+k x+4=0 has real roots.

Find the value of k so that the equation 2x^(2)-5x+k=0 has two equal roots.

Find the least integral value of k for which the equation x^(2)-2(k+2)x+12+k^(2)=0 has two different real roots.