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Math Help - Polynomials

  1. #1
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    Polynomials

    If \alpha and \beta are roots of the equation x^2+mx+n=0, find the roots of nx^2+(2n-m^2)x+n=0 in terms of \alpha and \beta
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    Quote Originally Posted by nerdzor View Post
    If \alpha and \beta are roots of the equation x^2+mx+n=0, find the roots of nx^2+(2n-m^2)x+n=0 in terms of \alpha and \beta
    From the first equation you can get n and m in terms of \alpha and \beta:

    \alpha \, \beta = n.
    \alpha + \beta = -m.

    Solve the second equation using the quadratic formula. Then replace n and m in terms of \alpha and \beta.
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    Help?

    Quote Originally Posted by mr fantastic View Post
    Solve the second equation using the quadratic formula. Then replace n and m in terms of \alpha and \beta.
    How do I do the quadratic formula with the 2nd equation? It gets really messy and I can't get it. Help?
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    Quote Originally Posted by nerdzor View Post
    How do I do the quadratic formula with the 2nd equation? It gets really messy and I can't get it. Help?
    Sorry, but messy in maths is like digging a hole with a spade. It can be done but it takes effort. Your effort, not mine.

    If you're genuinely stuck (as in you have absolutley no idea what to do) I or someone else will give additional assistance (but not with the manual labour).
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    Quote Originally Posted by mr fantastic View Post
    Sorry, but messy in maths is like digging a hole with a spade. It can be done but it takes effort. Your effort, not mine.

    If you're genuinely stuck (as in you have absolutley no idea what to do) I or someone else will give additional assistance (but not with the manual labour).
    But, instead of a spade you might try using a bobcat by noting that if \gamma and \delta are roots of the second equation, then

    \gamma \, \delta = 1
    \gamma + \delta = \frac{m^2}{n} - 2

    where I've obviously divided the second equation through by n first .....
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