Question

If two quadratic equations x² + ax + b = 0 and x² + bx + a = 0 (a ≠ 0) hava a common root. Find the value of a + b.
1. 1
2. -1
3. 2
4. 0

Answer 1

Correct Answer - Option 2 : -1

Given:

Two quadratic equations x2 + ax + b = 0 and x2 + bx + a = 0 (a ≠ 0) have a common root.

Calculation:

Let common root in both equations be α.

α satisfies both equation, so we put x = α in both equations 

⇒ α² + aα + b = 0     ----1

⇒ α2 + bα + a = 0     ----2

By equating both equations

⇒ α2 + aα + b = α2 + bα + a

⇒ aα + b = bα + a

⇒ α(a - b) = a - b

⇒ α = 1

Put α = 1 in equation 1

⇒ 1 + a + b = 0 

⇒ a + b =  - 1

∴ The value of a + b is - 1.