Mathematics

Problem

Let

a, b, c

be the lengths of the sides of a triangle (no two of them are equal) and

k \in R

. If the roots of the equation

x^2 + 2(a + b + c)x + 6k(ab + bc + ca) = 0

are real, then: (a)

k < \frac{2}{3}

(b)

k > \frac{2}{3}

(c)

k > 1

(d)

k < \frac{1}{4}