sextic

(%i1)

load ( odes ) $

(%i2)

eq : − x ^ 6 + x ^ 5 + 2 · x ^ 4 − 2 · x ^ 3 + x ^ 2 + 2 · x − 1 = 0 ;

- x^{6} + x^{5} + 2 x^{4} - 2 x^{3} + x^{2} + 2 x - 1 = 0

(%i3)

P ( x ) : = − x ^ 6 + x ^ 5 + 2 · x ^ 4 − 2 · x ^ 3 + x ^ 2 + 2 · x − 1 ;

P (x) := - x^{6} + x^{5} + 2 x^{4} + (- 2) x^{3} + x^{2} + 2 x - 1

(%i4)

solvet ( eq , x ) ;

[x = - 1, x = - \frac{\sqrt{3} %i - 1}{2}, x = \frac{\sqrt{3} %i + 1}{2}, x = \frac{2 \sqrt{7} \cos (\frac{atan (3^{\frac{3}{2}}) - 3 π}{3}) + 1}{3}, x = \frac{2 \sqrt{7} \cos (\frac{atan (3^{\frac{3}{2}}) - π}{3}) + 1}{3}, x = \frac{2 \sqrt{7} \cos (\frac{atan (3^{\frac{3}{2}}) + π}{3}) + 1}{3}]

(%i5)

wxplot2d ( [ P ( x ) ] , [ x , − 1 . 5 , 2 ] ) , wxplot_size = [ 640 , 480 ] $

Created with wxMaxima.

The source of this Maxima session can be downloaded here.