If p = (1111 ... up to n digits), then what is the value of 9p² + p?

The quadratic equation 3x² - (k² + 5k)x + 3k² - 5k = 0 has real roots of equal magnitude and opposite sign. Which one of the following is correct?

If a_n = n(n!), then what is a₁ + a₂ + a₃ +...+ a₁₀ equal to?

If p and q are the non-zero roots of the equation x² + px + q = 0, then how many possible values can q have?