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

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

We get $2 \ kg$ of pure butter less in Rs. $960$ if the price of pure butter increases by Rs. $40$ per $kg$. Find the original price of pure butter per kilogram.

The roots of a quadratic equation $6 x^{2}-13 x+6=0$ are .... .

If one of the roots of the equation $3x^{2} + 2kx - 3 = 0$ is $-\frac{1}{2}$,then find the value of $k$.

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