The value of the discriminant $D$ of the quadratic equation $x^{2} + 5x + 1 = 0$ is $\ldots \ldots \ldots \ldots .$

If the following quadratic equation has two equal and real roots,then find the value of $k$: $(k+1) x^{2}-2(k+3) x+(2 k+3)=0$

The hypotenuse of a garden in the shape of a right triangle is $1$ metre more than twice the shortest side. If the longer side containing the right angle is $7$ metres more than the shorter side,find the sides of the garden.

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 $x^{2}+6x+5=0$	$d. 16$

Find two consecutive even positive integers,the sum of whose squares is $244$.

Solve the following equation using the method of factorization and write its solution set: $\frac{8}{x+5} = \frac{3}{x-1} + \frac{1}{x-5}$