Which of the following equations has $\text{'}2\text{'}$ as a root?

If $\frac{1}{2}$ is a root of the equation $x^2+kx-\frac{5}{4}=0$, then the value of $k$ is:

Which of the following equations has the sum of its roots as $3$?

Value of $k$ for which the quadratic equation $2x^2-kx+k=0$ has equal roots is:

The quadratic equation $2x^2-\sqrt{5}x+1=0$ has:

${\left(x^2+1\right)}^2-x^2=0$ has: