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Math Help - Find quadratic equation through roots

  1. #1
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    Find quadratic equation through roots

    Question: Given that (alpha) and (beta) are roots of the quadratic equation 6x - 3x^2 = 4, find the equation whose roots are
    square root (alpha) and square root (beta)

    Sum of roots = 2
    Product of roots = 4/3

    How do I make it such that the sum of square root (alpha) and square root (beta) can substituted using the original sum of roots and product of roots to find it's value?

    Sorry, i'm not sure of how to input the math signs
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  2. #2
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    Re: Find quadratic equation through roots

    Quote Originally Posted by FailInMaths View Post
    Question: Given that (alpha) and (beta) are roots of the quadratic equation 6x - 3x^2 = 4, find the equation whose roots are
    square root (alpha) and square root (beta)

    Sum of roots = 2
    Product of roots = 4/3
    You know that the equation is x^2-(\sqrt{\alpha}+\sqrt{\beta})x+ \sqrt{\alpha\beta}=0

    Moreover, you know the value of (\sqrt{\alpha}+\sqrt{\beta})^2=\alpha+\beta+2\sqrt  {\alpha\beta}

    Evaluate those.
    Thanks from topsquark and FailInMaths
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  3. #3
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    Re: Find quadratic equation through roots

    Quote Originally Posted by Plato View Post
    You know that the equation is x^2-(\sqrt{\alpha}+\sqrt{\beta})x+ \sqrt{\alpha\beta}=0

    Moreover, you know the value of (\sqrt{\alpha}+\sqrt{\beta})^2=\alpha+\beta+2\sqrt  {\alpha\beta}

    Evaluate those.
    Thanks for replying, I did tried that method, but my answer is a long string of number. 2.160246899. How do I continue from there?
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  4. #4
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    Re: Find quadratic equation through roots

    Quote Originally Posted by FailInMaths View Post
    but my answer is a long string of number. 2.160246899. How do I continue from there?
    Frankly I don't how you get "a long string of number"

    Both \alpha~\&~\beta are rather simple complex numbers. That is part of this question I don't like.

    However, assuming we use the principal square roots. I got rather simple answer.
    Thanks from FailInMaths
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  5. #5
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    Re: Find quadratic equation through roots

    Quote Originally Posted by Plato View Post
    Frankly I don't how you get "a long string of number"

    Both \alpha~\&~\beta are rather simple complex numbers. That is part of this question I don't like.

    However, assuming we use the principal square roots. I got rather simple answer.
    square root (a + b +2square root (ab))
    = square root (2+2(4/3))
    = square root (14/3)
    = 2.160246899 on calculator

    I think there's something wrong with the variables of the question, I haven't learn simple complex numbers or principal square roots.
    I will check it out with my teacher, thanks for your help, you can mark this as solved now
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