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Thread: Polynomial/roots question [Mathematics Preliminary Extension 1]

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    Question Polynomial/roots question [Mathematics Preliminary Extension 1]

    The equation x3-bx2+cx-d = 0, where d>0, has roots α, ß and αß. Show that (c+d)2 = (b+1)2d.


    New to forums and not sure if this is how things are done. Sorry in advance!
    And thanks!
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    Re: Polynomial/roots question [Mathematics Preliminary Extension 1]

    Quote Originally Posted by Nktnet View Post
    The equation x3-bx2+cx-d = 0, where d>0, has roots α, ß and αß. Show that (c+d)2 = (b+1)2d.


    New to forums and not sure if this is how things are done. Sorry in advance!
    And thanks!
    How you have done it is just fine- just post any questions and in time I'm sure they will be answered.

    For this particular problem:

    Derive equations for the sum, sum for two at a time, and product of roots. [I will use a, B and aB as the roots] These will give you:
    1. (aB)^2=d
    2. a+B+aB= b
    3. aB(1+a+B)=c

    Adding 1 and 3 together we get

    c+d= aB+a^2 B+ aB^2 + (aB)^2

    Factorising:

    c+d= aB(1+a+B+aB)

    Squaring both sides we get

    (c+d)^2= (aB)^2 (1+a+B+aB)^2

    Now we sub in our initial pro-numerals

    (c+d)^2 = d(1+b)^2
    Last edited by HoldingOn; 20 Sep 2018 at 9:33 PM.
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    Re: Polynomial/roots question [Mathematics Preliminary Extension 1]

    Thank you so much!
    That makes a lot of sense and was really easy to follow.
    HoldingOn likes this.

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