Given that 2 is a root of the equation 3x² - p(x + 1) = 0 and that the equation px² - qx + 9 = 0 has equal roots, find the values of p and q.

Since, 2 is the root hence, it satisfies the equation 3x² - p(x + 1) = 0.

⇒ 3(2)² - p(2 + 1) = 0

⇒ 3(4) - 3p = 0

⇒ 3p = 12

⇒ p = 4.

Substituting value of p in px² - qx + 9 = 0

⇒ 4x² - qx + 9 = 0

Comparing 4x² - qx + 9 = 0 with ax² + bx + c = 0 we get,

a = 4, b = -q and c = 9.

Since equation has equal roots,

∴ D = 0

⇒ (-q)² - 4.(4).(9) = 0

⇒ q² - 144 = 0

⇒ q² = 144

⇒ q = 12 or -12.

Hence, p = 4 and q = 12 or -12.