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Thread: Polynomials zzz

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    Cadet JustRandomThings's Avatar
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    Polynomials zzz

    Hey every1 thnx in advance!

    Denote a-alpha b-beta c-gamma

    a,b and c are roots of the polynomial x^3-2x^2-5x-1=0. Find the equation with the roots 1/√a , 1/√b and 1/√c (1 on root alpha, 1 on root beta, 1 on root Gamma)
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    Re: Polynomials zzz

    Quote Originally Posted by JustRandomThings View Post
    Hey every1 thnx in advance!

    Denote a-alpha b-beta c-gamma

    a,b and c are roots of the polynomial x^3-2x^2-5x-1=0. Find the equation with the roots 1/√a , 1/√b and 1/√c (1 on root alpha, 1 on root beta, 1 on root Gamma)
    x=a,b,c
    y= 1/sqrt(a) etc
    y = 1/sqrt(x)
    y^2 = 1/x
    x = 1/y^2

    Sub into the equation
    (1/y^2)^3 - 2(1/y^2)^2 - 5(1/y^2) - 1 = 0
    1/y^6 - 2/y^4 - 5/y^2 - 1 = 0
    1 - 2y^2 - 5y^4 - y^6 = 0

    Therefore
    x^6 + 5x^4 + 2x^2 - 1 = 0
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    Re: Polynomials zzz

    Quote Originally Posted by pikachu975 View Post
    x=a,b,c
    y= 1/sqrt(a) etc
    y = 1/sqrt(x)
    y^2 = 1/x
    x = 1/y^2

    Sub into the equation
    (1/y^2)^3 - 2(1/y^2)^2 - 5(1/y^2) - 1 = 0
    1/y^6 - 2/y^4 - 5/y^2 - 1 = 0
    1 - 2y^2 - 5y^4 - y^6 = 0

    Therefore
    x^6 + 5x^4 + 2x^2 - 1 = 0
    Hey can I ask how you obtained y=1/sqrt(x)
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    Re: Polynomials zzz

    If you have roots x=a, x=b, x=c and you want 1/sqrt(a), 1/sqrt(b) and 1/sqrt(c), subbing x=a, x=b and x=c into y=1/sqrt(x) will yield your desired roots
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    Re: Polynomials zzz

    Quote Originally Posted by fluffchuck View Post
    If you have roots x=a, x=b, x=c and you want 1/sqrt(a), 1/sqrt(b) and 1/sqrt(c), subbing x=a, x=b and x=c into y=1/sqrt(x) will yield your desired roots
    Ahh I see now thanks Fluff and Pikachoooo!
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    Re: Polynomials zzz

    Quote Originally Posted by JustRandomThings View Post
    Ahh I see now thanks Fluff and Pikachoooo!
    Learnt this method in 4u but I guess you could probably use it in whichever maths this is.
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