Question

If 1 is a root of the equation ay² + ay + 3 = 0 and y² + y + b = 0 then find the value of ab.

Answer 1

It is given that y = 1 is a root of the equation ay² + ay + 3 = 0 

∴ a × (1)² + a × 1 + 3 = 0 

⇒ a + a + 3 = 0 

⇒ 2a + 3 = 0 

⇒ `a = -3/2` 

Also, y = 1 is a root of the equation y² + y + b = 0 

∴ (1)² + 1 + b = 0 

⇒ 1 + 1 + b = 0 

⇒ b + 2 = 0 

⇒ b = –2 

∴ `ab = (-3/2) xx (-2) = 3` 

Hence, the value of ab is 3.