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The roots of the equation (b – c) x² + (c – a) x + (a – b) = 0 are equal, then (a) 2a = b + c (b) 2c = a + b (c) b = a + c (d) 2b = a + c

The roots of the equation (b – c) x² + (c – a) x + (a – b) = 0 are equal, then
(a) 2a = b + c
(b) 2c = a + b
(c) b = a + c
(d) 2b = a + c

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8741 Points
2 months ago
Answer: d Explaination:Reason: 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

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