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Math Help - [SOLVED] Quadratic equation

  1. #1
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    [SOLVED] Quadratic equation

    In what interval can p+q be if we know that the sum of the squares of the roots of x^2+px+q=0 equals to 1 ( x_1^2+x_2^2=1).
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  2. #2
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    Quote Originally Posted by james_bond View Post
    In what interval can p+q be if we know that the sum of the squares of the roots of x^2+px+q=0 equals to 1 ( x_1^2+x_2^2=1).
    \left [-1, \sqrt{2} + \frac{1}{2} \right].
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  3. #3
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    Quote Originally Posted by NonCommAlg View Post
    \left [-1, \sqrt{2} + \frac{1}{2} \right].
    Thanks but could you go into more details? Thanks in advance!
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  4. #4
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    Quote Originally Posted by james_bond View Post
    Thanks but could you go into more details? Thanks in advance!
    there exists some t such that x_1=\cos t, \ x_2= \sin t. let x=\cos t + \sin t. we have p+q=-(x_1+x_2)+x_1x_2=\frac{1}{2}(x-1)^2 - 1. finally use the fact that -\sqrt{2} \leq x \leq \sqrt{2} to finish the proof.
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