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Math Help - Use the inverse function theorem to estimate the change in the roots

  1. #1
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    Use the inverse function theorem to estimate the change in the roots

    Let p(\lambda )=\lambda^3+a_2\lambda^2+a_1\lambda+a_0=(\lambda-x_1)(\lambda-x_2)(\lambda-x_3) be a cubic polynomial in 1 variable \lambda. Use the inverse function theorem to estimate the change in the roots 0<x_1<x_2<x_3 if a=(a_2,a_1,a_0)=(-6,11,-6) and a changes by \Delta a=0.01a.


    How can I use the inverse function theorem to estimate?
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  2. #2
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    Re: Use the inverse function theorem to estimate the change in the roots

    Hey ianchenmu.

    If you have a root, then the inverse function would set x = 0 and y = the root. Now if you can find where this happens with the inverse function theorem and do an approximate taylor expansion with a linear component, then you can estimate the changes in the roots.
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    Re: Use the inverse function theorem to estimate the change in the roots

    What \Delta a means? Can you give me a more complete answer? Thank you.
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    Re: Use the inverse function theorem to estimate the change in the roots

    Quote Originally Posted by chiro View Post
    Hey ianchenmu.

    If you have a root, then the inverse function would set x = 0 and y = the root. Now if you can find where this happens with the inverse function theorem and do an approximate taylor expansion with a linear component, then you can estimate the changes in the roots.
    What \Delta a means? Can you give me a more complete answer? Thank you.
    Follow Math Help Forum on Facebook and Google+

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