Given: Two Quadratic Equations and

Required: to find the common root of the given Quadratic Equations

Let the common root be α

Α is the root of x²–bx + c = 0

∴ x²–bx + c = 0

⇒ α²–bα + c = 0 -eq(1)

Also, α is the root of x² + bx–a = 0

∴ α² + bα–a = 0 -eq(2)

Here, eq(1) = eq(2)

∴ α² + bα–a = α²–bα + c

⇒ 2bα = c + a

⇒ α =

∴ The common root is α =

∴ Correct Option is - Option(A)