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Math Help - Quadratic question Q3

  1. #1
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    Quadratic question Q3

    Find the range of values of k if the equation Xsquare+(4K-2)X+(5Ksqure-4)=0 has 2 real and distinct roots of opposite signs.

    Thanks.

    How do I type X squre in the text box? Thank.
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  2. #2
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    Quote Originally Posted by yeoky View Post
    How do I type X squre in the text box? Thank.
    x^2 is the usual convention.

    Note: The latex code for x^2 is [tex]x^2[/tex]. See here: http://www.mathhelpforum.com/math-he...-tutorial.html
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  3. #3
    MHF Contributor red_dog's Avatar
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    The roots are real and distinct \Rightarrow\Delta>0

    \Delta=b^2-4ac=4(-k^2-4k+5)

    k_1=-5, \ k_2=1\Rightarrow k\in(-5,1) (1)

    The roots are of opposite signs \Rightarrow x_1x_2<0

    x_1x_2=5k^2-4<0\Rightarrow k\in\left(-\frac{2}{\sqrt{5}},\frac{2}{\sqrt{5}}\right) (2)

    From (1) and (2) \Rightarrow x\in\left(-\frac{2}{\sqrt{5}},\frac{2}{\sqrt{5}}\right)
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