The value of the discriminant of the quadratic equation $x^{2}-8x+15=0$ is ...... .

Find the discriminant of the following quadratic equation: $3x^{2} - 12x + 16 = 0$.

$A$ two-digit number is such that the product of its digits is $10$. When $27$ is added to the original number,the new number obtained is the same as the number obtained by interchanging the digits of the original number. Determine the number.

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

Examine whether the following equation is quadratic or not: $9x = 3x^3$.

Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $2x^{2} - 2\sqrt{6}x + 3 = 0$