Odpowiedź:
[tex]d)\\\\x^4-x^3-7x^2+13x-6=0\\\\x^4-x^3-7x^2+7x+6x-6=0\\\\x^3(x-1)-7x(x-1)+6(x-1)=0\\\\(x-1)(x^3-7x+6)=0\\\\(x-1)(x^3-x-6x+6-x^2+x^2)=0\\\\(x-1)(x^2(x-1)+x(x-1)-6(x-1)=0\\\\(x-1)(x-1)(x^2+x-6)=0\\\\(x-1)(x-1)(x^2+3x-2x-6)=0\\\\(x-1)(x-1)(x(x+3)-2(x+3))=0\\\\(x-1)(x-1)(x+3)(x-2)=0\\\\(x-1)^2(x+3)(x-2)=0\\\\(x-1)^2=0\ \ \ \ \vee\ \ \ \ x+3=0\ \ \ \ \vee\ \ \ \ x-2=0\\\\x-1=0\ \ \ \ \ \ \ \ \vee\ \ \ \ x=-3\ \ \ \ \ \ \vee\ \ \ \ x=2\\\\x=1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=-3\ \ \ \ \ \ \vee\ \ \ \ x=2[/tex]
[tex]e)\\\\x^4-4x^3+6x^2-4x+1=0\\\\x^4-x^3-3x^3+3x^2+3x^2-3x-x+1=0\\\\x^3(x-1)-3x^2(x-1)+3x(x-1)-(x-1)=0\\\\(x-1)(x^3-3x^2+3x+1)=0\\\\(x-1)(x-1)^3=0\\\\(x-1)^4=0\\\\x-1=0\\\\x=1[/tex]
[tex]f)\\\\x^4+3x^3-5x^2-12x+4=0\\\\x^4-2x^3+5x^3-10x^2+5x^2-10x-2x-4=0\\\\x^3(x-2)+5x^2(x-2)+5x(x-2)-2(x-2)=0\\\\(x-2)(x^3+5x^2+5x-2)=0\\\\(x-2)(x^3+2x^2+3x^2+6x-x-2)=0\\\\(x-2)(x^2(x+2)+3x(x+2)-(x+2))=0\\\\(x-2)(x+2)(x^2+3x-1)=0\\\\x-2=0\ \ \ \ \vee\ \ \ \ x+2=0\ \ \ \ \vee\ \ \ \ x^2+3x-1=0\\\\x=2\ \ \ \ \ \ \vee\ \ \ \ x=-2[/tex]
[tex]x^2+3x-1=0\\\\\Delta=b^2-4ac=3^2-4*1*(-1)=9+4=13\\\\\sqrt{\Delta}=\sqrt{13}\\\\\\x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-3-\sqrt{13}}{2*1}=\frac{-3-\sqrt{13}}{2}\\\\\\x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-3+\sqrt{13}}{2*1}=\frac{-3+\sqrt{13}}{2}[/tex]
