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Math Help - Question regarding Polynomials

  1. #1
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    Question regarding Polynomials

    Use the fourth degree equation ax^4 + bx^3 + cx^2 + dx + e = 0 whose roots are A,B,C,D to verify that

    1) the equation P(x/m) = 0 has roots m times those of P(x) = 0.

    Thank you.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by noobonastick View Post
    Use the fourth degree equation ax^4 + bx^3 + cx^2 + dx + e = 0 whose roots are A,B,C,D to verify that

    1) the equation P(x/m) = 0 has roots m times those of P(x) = 0.

    Thank you.
    Let x be a root of P(x)=0, put y=mx, then P(y/m)=P(x)=0, so mx is a root of P(x/m).

    CB
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    Let x be a root of P(x)=0, put y=mx, then P(y/m)=P(x)=0, so mx is a root of P(x/m).
    sorry I dont understand the logic... can you elaborate?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by noobonastick View Post
    sorry I dont understand the logic... can you elaborate?
    I have shown that if x is a root of P(x), then mx is a root of P(x/m).

    What else do you need?

    (note implicit assumption that m != 0)

    CB
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