What re the roots of the equation $$\left| {{x^2} - x - 6} \right| = x + 2$$?

The equation px² + qx + r = 0 (where p, q, r all are positive) has distinct real roots a and b. Which one of the following is correct?

The number of real roots for the equation $${x^2} + 9\left| x \right| + 20 = 0$$ is

If one root of the equation $x{}^2-kx+k=0$ exceeds the other by $2\sqrt{3}$ then which one of the following is a value of k?