Both the roots of the equation
(x - b)(x - c) + (x - b)(x - a) + (x - a)(x - b) = 0 Select the correct option.
A) dependent on a, b, c
B) always non real
C) always real
D) rational
E) None of these
Sol.(c) The equation is   3x2 - 2(a + b + c)x + (bc + ca + ab) = 0   The discriminant   D = 4(a + b + c)2 - 4.3.(bc + ca + ab)   = 4[a2 + b2 + c2 - ab - bc - ca]   = 2[(a2 - 2ab + b2) + (b2 - 2bc + c2) + (c2 - 2ca + a2)]   = 2[(a - b)2 + (b - c)2 + (c - a)2] ≥ 0   ∴ Roots are always real.   Answer always real
<result>C</result>
Both the roots of the equation
(x - b)(x - c) + (x - b)(x - a) + (x - a)(x - b) = 0