Question

The roots of the equation (b – c) x² + (c – a) x + (a – b) = 0 are equal, then:

Options

• 2a = b + c

• 2c = a + b

• b = a + c

• 2b = a + c

Answer 1

2b = a + c

Explanation:

Since roots are equal.

∴ D = 0 ⇒ b² – 4ac = 0

⇒ (c – a)² – 4(b – c) (a – b) = 0

⇒ c² – b² – 2ac – 4(ab – b² + bc) = 0

⇒ c + a – 2b = 0

⇒ c + a = 2b

⇒ c² + a² – 2ca – 4ab + 4b² + 4ac – 4bc = 0

⇒ c² + a² + 4b² + 2ca – 4ab – 4bc = 0

⇒ (c + a – 2b)² = 0

⇒ c + a – 2b = 0

⇒ c + a = 2b