If α and β are the roots of the equation ax2+bx+c=0 and Sn=αn+βn, then aSn+1+bSn+cSn−1is equal to

If α and β are the roots of the equation ax2+bx+c=0 and Sn=αn+βn, then aSn+1+bSn+cSn1is equal to

  1. A

    0

  2. B

    abc

  3. C

    a+b+c

  4. D

    None of these

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    Solution:

    Given, α and β are the roots of equation ax2+bx+c=0 and Sn=αn+βn
     α+β=ba and αβ=ca
    Now, Sn+1=αn+1+βn+1=αn+1+βn+1+αnβ+βnααnββnα=αn(α+β)+βn(α+β)αβαn1+βn1=(α+β)αn+βnαβαn1+βn1=baSncaSn1
     Sn+1=bSncSn1a aSn+1+bSn+cSn1=0.

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