pilne !!! rozwiaz rownania a) 2x-3) (x²-7x+10)=0 b) x²(x-3) (x²-4x) = 0 c) 27x³+125=0 d) x do 4 +3x³-4x²=0

[latex]a) (2x-3)(x^{2}-7x+10)=0\ \ 2(x-frac{3}{2})(x^{2}-5x-2x+10)=0\ \ 2(x-frac{3}{2})[x(x-5)-2(x-5)]=0\ \ 2(x-frac{3}{2})(x-2)(x-5)=0\ \ x-frac{3}{2}=0 vee x-2=0 vee x-5=0\ \ x=frac{3}{2} vee x=2 vee x=5\ \ \ b) x^{2}(x-3)(x^{2}-4x)=0\ x^{2}(x-3)*x(x-4)=0\ x^{3}(x-3)(x-4)=0\ x^{3}=0 vee x-3=0 vee x-4=0 vee \ x=0 vee x=3 vee x=4\ \ x=0 - pierwiastek trzykrotny[/latex] [latex]c) 27x^{3}+125=0\ \ 27(x^{3}+frac{125}{27})=0\ \ 27(x+frac{5}{3})(x^{2}-frac{5}{3}x+frac{25}{9})=0\ \ x+frac{5}{3}=0 vee x^{2}-frac{5}{3}x+frac{25}{9}=0\ \ x=-frac{5}{3} brak\ \ \ d) x^{4}+3x^{3}-4x^{2}=0\ x^{2}(x^{2}+3x-4)=0\ x^{2}(x^{2}+4x-x-4)=0\ x^{2}[x(x+4)-(x+4)]=0\ x^{2}(x-1)(x+4)=0\ x^{2}=0 vee x-1=0 vee x+4=0\ x=0 vee x=1 vee x=-4\ \ x=0 - pierwiastek dwukrotny[/latex]