Odpowiedź:
[tex]a)\\\\x(x+5)^2(x-1)=0\\\\x=0\ \ \ \ \vee\ \ \ \ (x+5)^2=0\ \ \ \ \vee\ \ \ \ x-1=0\\\\x=0\ \ \ \ \vee\ \ \ \ x+5=0\ \ \ \ \ \ \ \ \vee\ \ \ \ x=1\\\\x=0\ \ \ \ \vee\ \ \ \ x=-5\ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=1[/tex]
[tex]b)\\\\x^3+2x^2-9x-18=0\\\\x^2(x+2)-9(x+2)=0\\\\(x+2)(x^2-9)=0\\\\(x+2)(x-3)(x+3)=0\\\\x+2=0\ \ \ \ \vee\ \ \ \ x-3=0\ \ \ \ \vee\ \ \ \ x+3=0\\\\x=-2\ \ \ \ \ \ \ \vee\ \ \ \ x=3\ \ \ \ \ \ \ \ \vee\ \ \ \ x=-3[/tex]
[tex]c)\\\\x^3-6x^2-5x-14=0\\\\x^3-7x^2+x^2-7x+2x-4=0\\\\x^2(x-7)+x(x-7)+2(x-7)=0\\\\(x-7)(x^2+x+2)=0\\\\x-7=0\ \ \ \ \vee\ \ \ \ x^2+x+2=0\\\\x=7\ \ \ \ \ \ \ \ \vee\ \ \ \ \Delta=b^2-4ac=1^2-4\cdot1\cdot2=1-8=-7\ \ brak\ \ rozwiazania\\\\x=7[/tex]
[tex]d)\\\\4x^5+x^3=4x^3\\\\4x^5+x^3-4x^3=0\\\\4x^5-3x^3=0\\\\x^3(4x^2-3)=0\\\\x^3=0\ \ \ \ \vee\ \ \ \ 4x^2-3=0\\\\x=0\ \ \ \ \vee\ \ \ \ 4x^2=3\ \ /:4\\\\x=0\ \ \ \ \vee\ \ \ \ x^2=\frac{3}{4}\\\\x=0\ \ \ \ \vee\ \ \ \ x=\sqrt{\frac{3}{4}}\ \ \ \ \vee\ \ \ \ x=-\sqrt{\frac{3}{4}}\\\\x=0\ \ \ \ \vee\ \ \ \ x=\frac{\sqrt{3}}{2}\ \ \ \ \vee\ \ \ \ x=-\frac{\sqrt{3}}{2}[/tex]
