Rozwiązanie:
[tex]g(x)=6x^{4} +13x^{3} -5x^{2} -3x+1[/tex]
[tex]g(-\frac{1}{2} )=6*\frac{1}{16}-13*\frac{1}{8} -5*\frac{1}{4}+\frac{3}{2}+1=\frac{6}{16}-\frac{26}{16}-\frac{20}{16}+\frac{24}{16}+\frac{16}{16}=0[/tex]
[tex]g(\frac{1}{3})=\frac{6}{81} +\frac{13}{27}-\frac{5}{9}-1+1=\frac{2}{27}+\frac{13}{27}-\frac{15}{27}=0[/tex]
[tex]g(x)=(x-\frac{1}{3} )(x+\frac{1}{2} )(x^{2} +2x-1)[/tex]
[tex]\Delta=4-4*1*(-1)=8\\x_{1}=\frac{-2-2\sqrt{2} }{2}=-1-\sqrt{2}\\x_{2}=\frac{-2+2\sqrt{2} }{2}=-1+\sqrt{2}[/tex]
Zatem pierwiastki wielomianu to [tex]\frac{1}{3} ,-\frac{1}{2}, -1-\sqrt{2} , -1+\sqrt{2}[/tex]
