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Math Help - polynomial roots

  1. #1
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    polynomial roots

    the polynomial x^3 - 4x^2 + 5x - 1 = 0 has 3 roots a,b and y
    i. find the value of a + b + y
    ii. find the value of aby
    iii. find the equation of the polynomial with roots 2a, 2b and 2y


    i got 4 for i and 1 for ii
    are these right??
    how do you do iii.?
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  2. #2
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    Quote Originally Posted by deej813 View Post
    the polynomial x^3 - 4x^2 + 5x - 1 = 0 has 3 roots a,b and y
    i. find the value of a + b + y
    ii. find the value of aby
    iii. find the equation of the polynomial with roots 2a, 2b and 2y


    i got 4 for i and 1 for ii
    are these right?? Yes.
    how do you do iii.?
    If x^3 - 4x^2 + 5x - 1 = 0 has roots a, b and y then (x/2)^3 - 4(x/2)^2 + 5(x/2) - 1 = 0 has roots 2a, 2b and 2y.
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  3. #3
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    really?
    how do you work that out?
    do i simplify to
    x^3/8 - 4x^2/4 + 5x/2 -1 = 0 ??
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  4. #4
    ynj
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    Quote Originally Posted by deej813 View Post
    really?
    how do you work that out?
    do i simplify to
    x^3/8 - 4x^2/4 + 5x/2 -1 = 0 ??
    since if x=ais a root for f(x), then 2ais a root for f(\frac{x}{2})
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  5. #5
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    oh ok i get it
    thanks
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