Discussion and solve

**dhiab** · August 25th 2009, 05:35 AM

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

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

**red_dog** · August 25th 2009, 09:35 AM

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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