The roots of the equation $|x^2-x-6|=x+2$ are

What is the nature of the roots of the equation $a^2x^2 + (a + b)x - b^2 = 0$?

If the roots of the equation $\frac{1}{x + p} + \frac{1}{x + q} = \frac{1}{r}$ are equal in magnitude but opposite in sign,what is their product?

Let $S$ be the set of all possible integral values of $\lambda$ in the interval $(-3, 7)$ for which the roots of the quadratic equation $\lambda x^2 + 13x + 7 = 0$ are all rational numbers. Then the sum of the elements in $S$ is

The product of all the real roots of $x^2-8x+9-\frac{8}{x}+\frac{1}{x^2}=0$ is

Which of the following is not a root of $f(x) = x^3 - 11x^2 + 36x - 36$?