JEE Main 2019MathematicsQuadratic EquationEasyMCQ

JEE Main 2019 — Quadratic Equation Question with Solution

JEE Main 2019 (12 Jan Shift 1)

Question

If λ be the ratio of the roots of the quadratic equation in x, 3m2x2+mm-4x+2=0, then the least value of m for which λ+1λ=1, is :

Choose an option

Show full solutionCorrect option: D
Correct answer
D4-32

Step-by-step explanation

Let α and β are the roots of given equation 3m2x2+mm-4x+2=0.

∴α+β=-mm-43m2 &  αβ=23m2         .........i

Given αβ=λ    &   λ+1λ=1

⇒αβ+βα=1

⇒α+β2=3αβ

Using equation i, we get

-mm-43m22=3×23m2

⇒m=4±32

Hence, the least value of m is 4-32.

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About this question

This is a previous-year question from JEE Main 2019, covering the Quadratic Equation chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.