JEE Main 2021MathematicsQuadratic EquationMediumMCQ

JEE Main 2021 — Quadratic Equation Question with Solution

JEE Main 2021 (27 Aug Shift 2)

Question

The set of all values of k>-1, for which the equation 3x2+4x+32-(k+1)3x2+4x+33x2+4x+2+ k3x2+4x+22=0 has real roots, is:

Choose an option

Show full solutionCorrect option: B
Correct answer
B1,52

Step-by-step explanation

Let t=3x2+4x+2

⇒ t+12-k+1tt+1+kt2=0

⇒t2+2t+1-(k+1)t2-(k+1)t+kt2=0

⇒2t+1-kt-t=0

⇒ t1-k=-1

Replacing the value of t again

3x2+4x+2=t=1k-1

⇒3x2+4x+2k-3k-1=0

For real roots, D≥0

⇒16-4×3×2k-3k-1≥0

⇒6k-9k-1-4≤0

⇒ 2k-5k-1≤0 

⇒k∈(1,52]

 

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About this question

This is a previous-year question from JEE Main 2021, 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.