Consider the following statements in respect of the quadratic equation $$4(x - p)(x - q) - {r^2} = 0$$, where p, q and r are real numbers.

1. The roots are real.

2. The roots are equal, if p = q and r = 0.

Which of the above statements is/are correct?

How many real roots does the equation $${x^2} + 3\left| x \right| + 2 = 0$$ have?

What is the solution of x $$\le$$ 4, y $$\ge$$ 0 and x $$\le$$ $$-$$4, y $$\le$$ 0?

If $$\alpha$$ and $$\beta$$ are the roots of x² + x + 1 = 0, then what is $$\sum\limits_{j = 0}^3 {({\alpha ^j} + {\beta ^j})} $$ equal to?