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JEE Main 2026 · 4 Apr · Shift 2, Mathematics question 5

If the quadratic equation (λ+2)x2−3λx+4λ=0(\lambda+2)x^2-3\lambda x+4\lambda=0, λ≠−2\lambda\ne-2, has two positive roots, then the number of possible integral values of λ\lambda is:

Choose one option
Answer and worked solution

Official answer: B

Real roots. D=9λ2−16λ(λ+2)=−λ(7λ+32)≥0D=9\lambda^2-16\lambda(\lambda+2)=-\lambda(7\lambda+32)\ge0, so −327≤λ≤0-\frac{32}7\le\lambda\le0.

Both positive. Product 4λλ+2>0\frac{4\lambda}{\lambda+2}>0 and sum 3λλ+2>0\frac{3\lambda}{\lambda+2}>0 need λ>0\lambda>0 or λ<−2\lambda<-2.

Together λ∈[−327,−2)\lambda\in\left[-\frac{32}7,-2\right): the integers −4-4 and −3-3.

(B)

Topics:Location of roots
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