[latex]c) \ x^{3}+5 x^{2} -3x-15=0 \ x^{2} (x+5)-3(x+5)=0 \ (x+5)( x-3)^{2} =0 \ (x+5)(x- sqrt{3})(x+ sqrt{3)}=0 \ x_{1}=-5 \ x_{2}= sqrt{3} \ x_{3}=- sqrt{3} \ e) \ 2 x^{3}- x^{2} +2x-1=0 \ x^{2} (2x-1)+(2x-1)=0 \ (2x-1)( x^{2} +1)=0 \ x= frac{1}{2} \ x^{2} +1 eq 0 (sprzeczne) \ g) \ [/latex] [latex]5 x^{3}+ x^{2} -20x-4=0 \ x^{2} (5x+1)-4(5x+1)=0 \ (5x+1)( x^{2} -4)=0 \ (5x+1)(x-2)(x+2)=0 \ x_{1}=- frac{1}{5} \ x_{2} =2\ x_{3}=-2 \ [/latex] Zadanie 2. a) [latex]3 x^{3}+2 x^{2} -12x-8=0 \ x^{2} (3x+2)-4(3x+2)=0 \ (3x+2)( x^{2} -4)=0 \ (3x+2)(x-2)(x+2)=0 \ x_{1}=- frac{2}{3} \ x_{2}=2 \ x_{3}=2 [/latex] c) [latex]6 x^{3}+5 x^{2} +18x+15=0 \ x^{2} (6x+5)+3(6x+5)=0 \ (6x+5)( x^{2} +3)=0 \ x_{1}=-frac{5}{6} \ x^{2} eq -3 [/latex] e) [latex]12 x^{3}+8 x^{2} -75x-50=0 \ 4 x^{2} (3x+2)-25(3x+2)=0 \ (3x+2)(4 x^{2} -25)=0 \ (3x+2)(2x-5)(2x+5)=0 \ x_{1}=- frac{2}{3} \ x_{2}= frac{5}{2} \ x_{3}=- frac{5}{2} [/latex] g) [latex]10 x^{3}-35 x^{2} +2x-7=0 \ 5 x^{2} (2x-7)+(2x-7)=0 \ (2x-7)(5 x^{2} +1)=0 \ 2x-7=0 \ x= frac{7}{2} \ 5 x^{2} +1=0 \ 5 x^{2} =-1 \ x^{2} =- frac{1}{5} (sprzecznosc) [/latex]
Rozwiąż równania : a)3x^3+2x^2-12x-8=0 b)20x^3-12x^2-5x+3=0 c)6x^3+5x^2+18x+15=0 d)10x^3-15x^2+2x-3=0 e)12x^3+8x^2-75x-50=0 f)27x^3+45x^2-12x-20=0 g)10x^3-35x^2+2x-7=0 poproszę krok po kroku jak to bd :)...
