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

Obtain the roots of the following equation using the method of 'completing the square': $3y^{2} + 7y - 20 = 0$.

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

Had Ajita scored $10$ more marks in her mathematics test out of $30$ marks,$9$ times these marks would have been the square of her actual marks. How many marks did she get in the test?

The formula for finding the value of $D$ (discriminant) for a quadratic equation $ax^2 + bx + c = 0$ is $\ldots \ldots \ldots \ldots.$

Examine whether the following equation is quadratic or not: $\frac{x-2}{x+2} - \frac{x+2}{x-2} = \frac{3}{7}$