The solution set of $x^{2}+5x+6=0$ is $\ldots \ldots \ldots \ldots.$

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 ..... .

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

Solve the equation $x^{2}-8x-21=0$ using the quadratic formula.

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 the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2} + x - 3 = 0$