The value of the discriminant of the quadratic equation $5x^{2} + x + 2 = 0$ is ..... .

If the value of the discriminant of a quadratic equation $6x^{2}-x-k=0$ is $25$,then $k = \ldots$

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2} = 9$.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + 12x + 9 = 0$.

Find whether the following equation has real roots. If real roots exist,find them.
$8 x^{2}+2 x-3=0$

State whether the quadratic equation $x^{2}-3x+4=0$ has two distinct real roots. Justify your answer.