Let b = a + c. Then the equation ax² + bx + c = 0 has equal roots, if

Given: b = a + c and the quadratic equation has equal roots

Here,

b²–4ac = 0 (∵ The quadratic equation has equal roots)

⇒ b²–4ac = 0

⇒ (a + c)²–4ac = 0 (∵ b = a + c)

⇒ a² + 2ac + c²–4ac = 0

⇒ a²–2ac + c² = 0

⇒ (a–c)² = 0

Applying sq.rt on both sides

⇒ √(a–c)² = √0

⇒ a–c = 0

⇒ a = c

∴ a = c

∴ Correct option is -Option (A)