##### Real number solutions

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What are the real number solutions of the equation 4x^5 - 52x^3 + 120x = 12x^4 - 36x^4

May 20th, 2015

$4x^5 - 52x^3 + 120x = 12x^4 - 36x^4\\ 4x^5 - 52x^3 + 120x = -24x^4\\ 4x^5+24x^4 - 52x^3 + 120x = 0\\ 4x(x^4+6x^3 - 13x^2 + 30)=0\\ x(x^4+6x^3 - 13x^2 + 30)=0\\$

x = 0 or $x^4+6x^3 - 13x^2 + 30=0$

So, x = 0 is a solution.

The equation of degree 4 does not have rational roots.

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May 20th, 2015

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May 20th, 2015

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