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 n is a root of the equation x² + px + m = 0 and m is a root of the equation x² + px + n = 0, where m ≠ n, then what is the value of p + m + n?

What is the number of real roots of the equation (x - 1)² + (x - 3)² + (x - 5)² = 0?