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Math Help - Discussion and solve

  1. #1
    Super Member dhiab's Avatar
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    Discussion and solve

    Solve and discussed by the values of real m this equation:

    m^2 x^4 + 18mx^3 + \left( {2m - 175} \right)x^2 - 78x - 8 = 0
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  2. #2
    MHF Contributor red_dog's Avatar
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    The equation can be written as

    m^2x^4+(18x^3+2x^2)m-175x^2-78x-8=0

    \Delta=b^2-4ac=4x^4(16x+3)^2

    m_1=-\frac{25}{x}-\frac{4}{x^2}, \ m_2=\frac{7}{x}+\frac{2}{x^2}

    Then the equation can be factorize:

    x^4\left(m+\frac{25}{x}+\frac{4}{x^2}\right)\left(  m-\frac{7}{x}-\frac{2}{x^2}\right)=0

    or (mx^2+25x+4)(mx^2-7x-2)=0

    Now you have to solve and discuss two quadratic equations:

    mx^2+25x+4=0 and mx^2-7x-2=0.

    Can you do that?
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