JEE Main 2019MathematicsQuadratic EquationMediumMCQ

JEE Main 2019 — Quadratic Equation Question with Solution

JEE Main 2019 (08 Apr Shift 2)

Question

If three distinct numbers a, b, c are in G.P. and the equations ax2+2bx+c=0 and dx2+2ex+f=0 have a common root, then which one of the following statements is correct?

Choose an option

Show full solutionCorrect option: A
Correct answer
Ada,eb,fc are in A.P.

Step-by-step explanation

∵ a, b, c are in G.P. ⇒b2=ac …(i)
Equation ax2+2bx+c=0
Hence, D=4b2-4ac=0 ∵b2=ac
⇒ equation has equal roots ⇒ roots are =-ba, -ba ( ∵ sum of roots α+α=-2ba )
∵ Both equations have one root in common.
∴ Common root is -ba. It will satisfy equation.
∴d-ba2+2e-ba+f=0⇒db2-2aeb+a2f=0
⇒dac-2aeb+a2f=0 ∵b2=ac
⇒dc-2aeb+af=0
⇒dcac-2ebac+afac=0 (dividing by ac )
⇒da-2ebb2+fc=-⇒da+fc=2eb
⇒da,eb,fc are in A.P.

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About this question

This is a previous-year question from JEE Main 2019, 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.