Find the discriminant for following equation and hence, decide if the equation has two distinct roots, two equal roots or no real roots.

$2x^2-7x+8=0$

Find the discriminant for following equation and hence, decide if the equation has two distinct roots, two equal roots or no real roots.

$3x^2+10x-2=0$

Use the discriminant to determine the nature of the roots of $2-5x=\frac{4}{x}$.

Find the values of $k$ for which the following equations have two equal roots.

$x^2+kx+4=0$

Find the values of $k$ for which the following equations have two equal roots.

$4x^2+4(k-2)x+k=0$

Find the values of $k$ for which the following equations have two equal roots.

$(k+2)x^2+4k=(4k+2)x$

Find the values of $k$ for which the following equations have two equal roots.

$x^2-2x+1=2k(k-2)$

Find the values of $k$ for which the following equations have two equal roots.

$(k+1)x^2+kx-2k=0$