The lengths of the sides forming the right angle of a right-angled triangle are $x \, m$ and $(x+2) \, m$. If the area of the triangle is $84 \, m^2$,find the lengths of the sides which form the right angle.

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

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2}-6x+2=0$.

Write whether the following statements are true or false. Justify your answers.
$(i)$ If the coefficient of $x^{2}$ and the constant term have the same sign and if the coefficient of $x$ term is zero,then the quadratic equation has no real roots.
$(ii)$ Every quadratic equation has at least two roots.

Find the roots of the quadratic equation by using the quadratic formula: $-x^{2}+7x-10=0$.

If $64$ is the discriminant of $k x^{2}-4 x-4=0$,then the value of $k$ is ...........