JEE Main 2022MathematicsQuadratic EquationHardMCQ

JEE Main 2022 — Quadratic Equation Question with Solution

JEE Main 2022 (28 Jun Shift 2)

Question

Let fx be a quadratic polynomial such that f-2 +f3=0. If one of the roots of fx=0 is -1, then the sum of the roots of fx=0 is equal to

Choose an option

Show full solutionCorrect option: A
Correct answer
A113

Step-by-step explanation

Let fx=ax2+bx+c

Given, f-2+f3=0

⇒4a-2b+c+9a+3b+c=0

⇒  13a+b+2c=0       ...i

Since -1 is a root of fx=0. So, f-1=0

⇒a-b+c=0      ...ii

On solving equations i & ii, we get

11a+3b=0  ⇒-ba=113

Now, we know that sum of the roots of ax2+bx+c=0 is -ba.

∴ The sum of the roots of fx=0 is 113.

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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.