Find the discriminant of the following quadratic equation: $\sqrt{5} x^{2}-3 \sqrt{3} x-2 \sqrt{5}=0$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $4x^{2} - 5x + k = 0$.

Which of the following groups correctly matches the data of Part $I$ with the data of Part $II$?

Part $I$	Part $II$
$1.$ The discriminant of $x^{2}+5x+6=0$	$a. 1$
$2.$ The discriminant of $x^{2}+5x+4=0$	$b. 9$
$3.$ The discriminant of $x^{2}+4x+3=0$	$c. 4$
$4.$ The discriminant of $x^{2}+6x+5=0$	$d. 16$

State whether the quadratic equation $(x-\sqrt{2})^{2}-2(x+1)=0$ has two distinct real roots. Justify your answer.

The formula for finding the value of $D$ (discriminant) for a quadratic equation $ax^2 + bx + c = 0$ is $\ldots \ldots \ldots \ldots.$

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.