Let , , be the sides of a triangle, with no two equal, and let . If the roots of are…

MATHEMATICS · Multi correct · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

Let

a

,

b

,

c

be the sides of a triangle, with no two equal, and let

\lambda\in\mathbb{R}

. If the roots of

x^2+2(a+b+c)x+3\lambda(ab+bc+ca)=0

are real, then: (1)

\lambda<\frac43

(2)

\lambda<\frac53

(3)

\lambda\in\left(\frac13,\frac53\right)

(4)

\lambda\in\left(\frac43,\frac53\right)

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