Correct Answer: C
Explanation:
The given equation can be written as
3 x2 – 2x (a + b + c) + bc + ca + ab = 0
Disc. = 4 (a + b + c)2 – 12 (bc + ca + ab)
= 4 [(a + b + c)2 – 3 (bc + ca + ab)]
= 4 [a2 + b2 + c2 – bc - ca - ab)
= 2 [2a2 + 2b2 + 2c2 – 2bc - 2ca -2ab)
= 2 [(a – b)2 + (b - c)2 + (c – a)2] ≥ 0
roots are always real.