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Math Help - quadratic equation, A.P. and G.P. related problem problem

  1. #1
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    quadratic equation, A.P. and G.P. related problem problem

    if ax2+2bx+c=0 and a1x2+2b1x+c1 have a common root and
    a/a1 ,b/b1 ,c/c1 are in A.P.

    show that a1,b1,c1 are in G.P.



    I know the mean formula of A.P. i.e. the middle term is the mean of the other two.

    any hints of which formula of G.P. to use and how to solve???
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: quadratic equation, A.P. and G.P. related problem problem

    What does A.P and G.P mean? (sorry I'm not from here)
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  3. #3
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    Re: quadratic equation, A.P. and G.P. related problem problem

    A.P. means arithmetic progression

    G.P. means geometric progression
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  4. #4
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    Re: quadratic equation, A.P. and G.P. related problem problem

    thank you i got the answer.

    let the AP be
    (A-D) , (A), (A+D)

    then
    a=a1(A-D)
    b=b1(A)
    c=c1(A+D)
    one root is common so
    putting these values in the formula
    (c1a2-c2a1)^2 = (a1b2-a2b1)(b1c2-b2c1)

    we get the required proof.

    thank you very much
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