The value of the discriminant of the quadratic equation $4x^{2} + 20x + 25 = 0$ is $\ldots \ldots \ldots \ldots .$

State whether the quadratic equation $x(1-x)-2=0$ has two distinct real roots. Justify your answer.

The value of discriminant $D$ for the equation $(3x - 14)^2 = 0$ is ........

State whether the following statements are true or false. Justify your answers.
$(i)$ Every quadratic equation has exactly one root.
$(ii)$ Every quadratic equation has at least one real root.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $5x^{2} - 4\sqrt{5}x + 4 = 0$.

Find whether the following equation has real roots. If real roots exist,find them.
$\frac{1}{2x-3} + \frac{1}{x-5} = 1, x \neq \frac{3}{2}, 5$