Find the set of all real values of \( \lambda \) such that the root...

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Find the set of all real values of \( \lambda \) such that the root of the equation \( x^{2}+2(a+b+c) x+3 \lambda(a b+b c+c a)=0 \) are always real for any choice of \( a, b, c(w h e r e a, b, c \) represents sides of scalene triangle).

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(A) \( \left(-\infty, \frac{4}{3}\right) \)
(B) \( \left(\frac{4}{3}, \infty\right) \)
(C) \( \left(\frac{1}{3}, \frac{5}{3}\right) \)
(D) \( \left(\frac{4}{3}, \frac{5}{3}\right) \)
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