If $3$ is a root of the quadratic equation $x^{2}-kx+6=0$,then $k = \ldots$

Obtain the roots of the following quadratic equation by using the quadratic formula: $6x^{2} + x - 2 = 0$.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $\frac{1}{4} x^{2} - 2x + 1 = 0$.

If both the roots of a quadratic equation $kx^{2} + 4x + 1 = 0$ are equal,then $k = \ldots$

If the value of the discriminant of the quadratic equation $x^{2}-10x+(2k-1)=0$ is $40$,then $k = \ldots$.

$120$ 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.