JEE Main 2014MathematicsQuadratic EquationMediumMCQ

JEE Main 2014 — Quadratic Equation Question with Solution

JEE Main 2014 (09 Apr Online)

Question

If 1α,1β  are the roots of the equation ax2+bx+1=0, a≠0, a,b∈R, then the equation xx+b3+a3-3abx=0 has roots:

Choose an option

Show full solutionCorrect option: D
Correct answer
Dα32 and β32

Step-by-step explanation

ax2+bx+1=0 has roots 1α,1β

⇒   1α+1β=-ba      ...1

1αβ=1a    ...2

xx+b3+a3-3abx=0

⇒ x2+b3-3abx+a3=0

Multiply and divide with a3, we get

⇒   x2+a3b3a3-31abax+a3=0
From equations 1 & 2,
⇒   x2+αβ3/2-α1/2+β1/23αβ3-31αβα+βαβx+αβ3/2=0

⇒  x2-α3/2+β3/2x+α3/2β3/2=0

Roots are α32 and β32.

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About this question

This is a previous-year question from JEE Main 2014, 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.