The value of discriminant $D$ for the equation $(x+2)(x-5)=0$ is ............

State whether the quadratic equation $2 x^{2}+x-1=0$ has two distinct real roots. Justify your answer.

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

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2}-2x-15=0$.

If both the roots of a quadratic equation $ax^2 + bx + c = 0$ $(a \neq 0)$ are equal,then ..... .

For a quadratic equation,if $\ldots \ldots \ldots \ldots$ then both the roots of an equation are distinct and real.