JEE Advance - Mathematics (2006 - No. 16)
Let $$a,\,b,\,c$$ be the sides of triangle where $$a \ne b \ne c$$ and $$\lambda \in R$$.
If the roots of the equation $${x^2} + 2\left( {a + b + c} \right)x + 3\lambda \left( {ab + bc + ca} \right) = 0$$ are real, then
If the roots of the equation $${x^2} + 2\left( {a + b + c} \right)x + 3\lambda \left( {ab + bc + ca} \right) = 0$$ are real, then
$$\lambda < {4 \over 3}$$
$$\lambda > {5 \over 3}$$
$$\lambda \in \left( {{1 \over 3},\,{5 \over 3}} \right)$$
$$\lambda \in \left( {{4 \over 3},\,{5 \over 3}} \right)$$