JEE Main 2023MathematicsQuadratic EquationMediumMCQ

JEE Main 2023 — Quadratic Equation Question with Solution

JEE Main 2023 (01 Feb Shift 1)

Question

Let
S=x:x∈ℝ and 3+2x2-4+3-2x2-4=10. Then nS is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B4

Step-by-step explanation

Given:

S=x:3+2x2-4+3-2x2-4=10

Now,

3-2=3+23-23+2=13+2

So,

3+2x2-4+3-2x2-4=10

⇒3+2x2-4+13+2x2-4=10

Put 3+2x2-4=u, then

u+1u=10

⇒u2-10u+1=0

⇒u=10±100-42

⇒u=5±24

⇒u=5±232

⇒u=3±22

⇒3+2x2-4=3±22

So, 3+2x2-4=3+22 and 3+2x2-4=13+22

Therefore,

x2-4=2 & x2-4=-2

⇒x=±6 & x=±2

So, S=6, 2, -6, -2

Hence, nS=4

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About this question

This is a previous-year question from JEE Main 2023, 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.