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