If $81$ is the discriminant of $2x^{2} + 5x - k = 0$,then the value of $k$ is ..............

Examine whether the following equation is quadratic or not: $(2x + 1)(3x + 2) = 6(x - 1)(x - 2)$

Find the discriminant of the following quadratic equation: $9x^{2} - bx + 3 = 0$.

If the roots of the quadratic equation $3x^{2} + 2\sqrt{5}x - 5 = 0$ exist,find them using the method of completing the square.

$120$ kites were divided equally among a certain number of children in a school. If there were $4$ children fewer,each child would have received $1$ kite more. Find the number of children.

The quadratic equation having roots $-1$ and $2$ is .... .