If the roots of the equation a2+bx+c = 0 are of the formk+1k and k+2k+1, then a+b+c2 is equal to

If the roots of the equation a2+bx+c = 0 are of the formk+1k and k+2k+1, then a+b+c2 is equal to

  1. A

    b2-4ac

  2. B

    b2-2ac

  3. C

    2b2-ac

  4. D

    Σa2

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    Solution:

    we have.k+1k+k+2k+1=ba..................(i)
    and k+1kk+2k+1=ca……………………….(ii)
    From Eq. (i), 
    1+1k+1+1k+1=ba
     2+1k+1k+1=ba…………………..(iii)
    From Eq. (ii),
    k+2k=ca1+2k=ca 2k=ca1k=2aca
    Now, on substituting the value of kin Eq. (iii), we get
    2+ca2a+12aca+1=ba

     2+ca2a+caa+c=ba
     2(2a)(a+c)+(ca)(c+a)+2a(ca)2a(a+c)=ba a2+c2+6ac=2ab2bc a2+b2+c2+2ab+2bc+2ca=b24ac (a+b+c)2=b24ac

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