JEE Main 2023MathematicsQuadratic EquationHardMCQ

JEE Main 2023 — Quadratic Equation Question with Solution

JEE Main 2023 (01 Feb Shift 2)

Question

The number of integral values of k, for which one root of the equation 2x2-8x+k=0 lies in the interval 1,2 and its other root lies in the interval 2,3, is : 

Choose an option

Show full solutionCorrect option: C
Correct answer
C1

Step-by-step explanation

Let f(x)=2x2-8x+k=0

 

f(1)>0

f(2)<0

f(3)>0

Now, f(1)>0⇒2-8+k>0⇒k>6 ......(1)

f(2)<0⇒8-16+k<0⇒k<8 ......(2)

f(3)>0⇒18-24+k>0⇒k>6 ......(3)

From equations 1, 2 & 3,

k∈(6,8)

∴ Integral value of k=7

Therefore number of integral value of k is one

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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.