If the roots of (b – c) x2 + (c – a) x + (a – b) = 0 are real eq

1.	If the roots of (b – c) x2 + (c – a) x + (a – b) = 0 are real equal, then which of the following is true ?(1) 2b = a + c (2) 2a = b + c (3) 2c = a + b (4) 2b = a – c
Answer» Correct option: (1) 2b = a + c Explanation: (b – c)x² + (c – a) x + (a – b) = 0 for equal roots D = 0 (c – a)² – 4 (b – c) (a – b) = 0 c² + a² – 2ac – 4ba + 4b² + 4ac – 4bc = 0 c² + a²+ 4b² – 4ab – 4bc + 2ac = 0 (c + a – 2b)² = 0 c + a = 2b.

If the roots of (b – c) x2 + (c – a) x + (a – b) = 0 are real equal, then which of the following is true ?(1) 2b = a + c (2) 2a = b + c (3) 2c = a + b (4) 2b = a – c

Answer»

Correct option: (1) 2b = a + c

Explanation:

(b – c)x² + (c – a) x + (a – b) = 0

for equal roots

D = 0

(c – a)² – 4 (b – c) (a – b) = 0

c² + a² – 2ac – 4ba + 4b² + 4ac – 4bc = 0

c² + a²+ 4b² – 4ab – 4bc + 2ac = 0

(c + a – 2b)² = 0

c + a = 2b.

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If the roots of (b – c) x2 + (c – a) x + (a – b) = 0 are real equal, then which of the following is true ?(1) 2b = a + c (2) 2a = b + c (3) 2c = a + b (4) 2b = a – c

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