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Math Help - Polynomials with Fractional Powers

  1. #1
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    Polynomials with Fractional Powers

    Factor: x^(2/5) - 3x^(1/5) - 4 = 0
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    Quote Originally Posted by magentarita View Post
    Factor: x^(2/5) - 3x^(1/5) - 4 = 0
    Use a similar idea to that suggested here: http://www.mathhelpforum.com/math-he...lynomials.html
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    Quote Originally Posted by magentarita View Post
    Factor: x^(2/5) - 3x^(1/5) - 4 = 0
    Strictly speaking, that is not a polynomial: polynomials don't have fractional powers. But it can be made into one- let y= x^{1/5} and solve for y first, then solve x^{1/5}= y for x.
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    ok...

    I know how to solve this equation using the substitution method but is there another way?
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    Quote Originally Posted by magentarita View Post
    I know how to solve this equation using the substitution method but is there another way?
    You have to realise that it's a quadratic.

    Technically all methods for factorising involve this "substitution" - it's just whether you want to make it look a bit more pleasing to the eyes.

    You could just as easily write it as

    (x^{\frac{1}{5}})^2 - 3x^{\frac{1}{5}} -4

    which becomes (x^{\frac{1}{5}} - 4)(x^{\frac{1}{5}} + 1).
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    how about...

    Quote Originally Posted by Prove It View Post
    You have to realise that it's a quadratic.

    Technically all methods for factorising involve this "substitution" - it's just whether you want to make it look a bit more pleasing to the eyes.

    You could just as easily write it as

    (x^{\frac{1}{5}})^2 - 3x^{\frac{1}{5}} -4

    which becomes (x^{\frac{1}{5}} - 4)(x^{\frac{1}{5}} + 1).
    How about this:

    (5th root of x)^2 - 3(5th root of x) - 4 = 0
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    Quote Originally Posted by magentarita View Post
    How about this:

    (5th root of x)^2 - 3(5th root of x) - 4 = 0
    That's the exact same question, because \sqrt[5]{x} = x^{\frac{1}{5}}.
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    ok...

    Quote Originally Posted by Prove It View Post
    That's the exact same question, because \sqrt[5]{x} = x^{\frac{1}{5}}.
    I understand now. Thank you so much.
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