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Math Help - Roots of oolynomial equations

  1. #1
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    Roots of oolynomial equations

    Sorry if this is in the wrong section. I wasn't sure where it went!
    If you have an equation:
    <br />
x^2 + 4x + 7 = 0<br />
    Which has roots
    \alpha and \beta
    And you want an equation that has roots
    <br />
\alpha + 2\beta and \beta + 2\alpha<br />

    How would you go about this by substitution? Because if i do
    let u = \alpha + 2\beta
    Im going to get alpha in terms of beta and u...and if i sub this into the equation im going to still have beta :S...
    I know you can do it via sum of roots = -b/a etc but im told in this example to use substitution -,-.

    Thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by AshleyT View Post
    Sorry if this is in the wrong section. I wasn't sure where it went!
    If you have an equation:
    <br />
x^2 + 4x + 7 = 0<br />
    Which has roots
    \alpha and \beta
    And you want an equation that has roots
    <br />
\alpha + 2\beta and \beta + 2\alpha<br />

    How would you go about this by substitution? Because if i do
    let u = \alpha + 2\beta
    Im going to get alpha in terms of beta and u...and if i sub this into the equation im going to still have beta :S...
    I know you can do it via sum of roots = -b/a etc but im told in this example to use substitution -,-.

    Thanks.
    You don't, you use the information that if a and b are roots of x^2+ux+v then u=a+b and v=ab.

    CB
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    You don't, you use the information that if a and b are roots of x^2+ux+v then u=a+b and v=ab.

    CB
    Yeah , but annoyingly im not allowed to use that method in this question ..I have to use a substitution method.
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