If the roots of the equation x² - ax - bx - cx + bc + ca = 0 are equal, then which one of the following is correct?

Let α and β (α > β) be the roots of the equation x² - 8x + q = 0. If α² - β² = 16, then what is the value of q?

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