JEE Main 2022MathematicsQuadratic EquationMediumNumerical

JEE Main 2022 — Quadratic Equation Question with Solution

JEE Main 2022 (28 Jul Shift 1)

Question

The sum of all real values of x for which 3x2-9x+17x2+3x+10=5x2-7x+193x2+5x+12 is equal to

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Show full solutionCorrect answer: 6
Correct answer
6

Step-by-step explanation

Given,

3x2-9x+17x2+3x+10=5x2-7x+193x2+5x+12

⇒x2+3x+10+2x2-12x+7x2+3x+10=3x2+5x+12+2x2-12x+73x2+5x+12

⇒1+2x2-12x+7x2+3x+10=1+2x2-12x+73x2+5x+12

⇒2x2-12x+71x2+3x+10-13x2+5x+12=0

2x2-12x+7=0 Or 3x2+5x+12=x2+3x+10

For 2x2-12x+7=0

Sum of roots=122=6

Or 3x2+5x+12=x2+3x+10

⇒ 2x2+2x+2=0

⇒x2+x+1=0

No real roots as D=1-4<0

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About this question

This is a previous-year question from JEE Main 2022, 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.