The discriminant of the equation $3x^2 - 6x + 4 = 0$ is .............

Find the roots of the following quadratic equation by the method of completing the square: $2x^{2} + x + 4 = 0$.

The roots of $x^{2}+12x+36=0$ are ...........

The difference between the lengths of the sides of a right triangle which form the right angle is $7 \, cm$. If its perimeter is $30 \, cm$,find the lengths of the sides.

Find the roots of the following quadratic equation by the factorisation method:
$3x^{2} + 5\sqrt{5}x - 10 = 0$

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