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    The roots of the equation :
    9x^2+6x+1=4kx

    where k is real constant ,are denoted by \alpha&\beta

    a) Show that the equation whose roots are

    \frac{1}{\alpha} &\frac{1}{\beta}

    is x^2+6x+9=4kx



    I tried
    (x-\frac{1}{\alpha})(x-\frac{1}{\beta})=0

    and ended up with \alpha\beta x^2-(\alpha+\beta) x +1=0
    also in the initial equation given it factorises to a perfect square(3x+1)^2=4kx

    I cant see what to do next , any hints in the right direction will be helpful thanks
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    Do you know about the relationships between the roots of equations and the coefficients of a quadratic equation?

    For the equation ax^2+bx+c=0

    A + B = -b/a
    A*B=c/a
    (where A and B are roots)

    Put the first equation in the form ax^2+bx+c=0 and see if this gets you anywhere...
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    There is a standard process for this type of question.

    Suppose ax^2 + bx + c = 0 has two roots p and q

    Then p+q = -b/a and pq = c/a

    If you then want to construct new equation with 1/p and 1/q, you can quickly see that product of roots of this new equation = 1/pq.

    After a bit of faff you can work out (1/p) + (1/q) in terms of p+q and pq, which you know from initial equation.

    So you now know sum-of-roots and product-of-roots for new equation.

    So you can construct your new equation.
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    (Original post by ian.slater)
    There is a standard process for this type of question.

    Suppose ax^2 + bx + c = 0 has two roots p and q

    Then p+q = -b/a and pq = c/a

    If you then want to construct new equation with 1/p and 1/q, you can quickly see that product of roots of this new equation = 1/pq.

    After a bit of faff you can work out (1/p) + (1/q) in terms of p+q and pq, which you know from initial equation.

    So you now know sum-of-roots and product-of-roots for new equation.

    So you can construct your new equation.
    sorry but thats what I have done



    I multiplied through alphabeta .. however I think now you put it that way I understand what to do now ..the only think thats troubling me is the 4kx ?
    edit:thanks Ian slater ..now I reread your post I get it...
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    You could have done x = 1/a, so a = 1/x, then replaced for x and multiplied out.
 
 
 
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