If $-3$ is a solution of $2x^{2} + 5x + k = 0$,then $k = \ldots$

If one root of a quadratic equation $ax^2 + bx + c = 0$ is $\frac{-b + \sqrt{D}}{2a}$,then the other root is $\ldots \ldots \ldots \ldots$.

State whether the quadratic equation $2 x^{2}-6 x+\frac{9}{2}=0$ has two distinct real roots. Justify your answer.

Find the roots of the following quadratic equation by the factorisation method:
$2x^{2} + \frac{5}{3}x - 2 = 0$

Find the roots of the following quadratic equation by the factorisation method:
$3x^{2} + 5\sqrt{5}x - 10 = 0$

The name of the Indian mathematician who gave the formula for finding the roots of the quadratic equation $ax^2 + bx + c = 0$ by the method of completing the square is ..... .