If 1 is a root of the equations ay² + ay + 3 = 0 and y² + y + b = 0, then ab equals:

ay² + ay + 3 = 0
As 1 is root then ⇒ a(1)² + a(1) + 3 = 0 ⇒ a + a = -3 ⇒ 2a = -3 ⇒ a = -3/2
y² + y + b = 0 ⇒ (1)² + 1 + b = 0 ⇒ 2 + b = 0 ⇒ b = -2; ∴ ab = -3/2 × -2 = 3