Question

If x = –2 is the common solution of quadratic equations ax² + x – 3a = 0 and x² + bx + b = 0, then find the value of a²b.

Answer 1

Given quadratic equations are

ax² + x – 3a = 0  ...(i)

x² + bx + b = 0  ...(ii)

Since, given x = –2 is the common solution of above quadratic equation.

∴ From equations (i),

a(–2)² + (–2) – 3a = 0

⇒ 4a – 2 – 3a = 0

⇒ a = 2

From equation (ii),

(–2)² + b(–2) + b = 0

⇒ 4 – 2b + b = 0

⇒ b = 4

Now, a²b = (2)² × 4 = 4 × 4 = 16