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

$\displaystyle m^2 x^4 + 18mx^3 + \left( {2m - 175} \right)x^2 - 78x - 8 = 0$

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- Aug 25th 2009, 05:35 AMdhiabDiscussion and solve
**Solve and discussed by the values of real m this equation:**

$\displaystyle m^2 x^4 + 18mx^3 + \left( {2m - 175} \right)x^2 - 78x - 8 = 0$ - Aug 25th 2009, 09:35 AMred_dog
The equation can be written as

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

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

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

Then the equation can be factorize:

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

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

Now you have to solve and discuss two quadratic equations:

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

Can you do that?