rozwiąż równanie wielomianowe : (x do kwadratu -2 ) (5-3x)=0  (5x do kwadratu -25y=30) *(-3x do kwadratu -6x +24 )=0 

[latex](x^2-2)(5-3x)=0\\x^2-2=0 vee 5-3x=0\\x^2=2 vee 3x=5\\x=-sqrt2 vee x=sqrt2 vee x=frac{5}{3}[/latex] [latex](5x^2-25x+30)(-3x^2-6x+24)=0\\1^o 5x^2-25x+30=0 /:5 vee 2^o -3x^2-6x+24=0 /:(-3)\\1^o x^2-5x+6=0\\Delta=(-5)^2-4cdot1cdot6=25-24=1; sqrtDelta=sqrt1=1\\x_1=frac{5-1}{2cdot1}=frac{4}{2}=2 veex_2=frac{5+1}{2cdot1}=frac{6}{2}=3\\2^o x^2+2x-8=0\\Delta=2^2-4cdot1cdot(-8)=4+32=36; sqrtDelta=sqrt{36}=6\\x_3=frac{-2-6}{2cdot1}=frac{-8}{2}=-4 vee x_4=frac{-2+6}{2cdot1}=frac{4}{2}=2[/latex] [latex]x=2 vee x=3 vee x=-4\\\©DRK[/latex]

zad. 1 [latex](x^2-2)(5-3x)=0[/latex] [latex]x^2-2=0[/latex] lub [latex] 5-3x=0[/latex] [latex]x^2-2=0[/latex] [latex]x^2=2[/latex] [latex]x=sqrt{2}[/latex] lub [latex]x=-sqrt{2}[/latex] [latex]5-3x=0[/latex] [latex]-3x=-5[/latex] [latex]x=1frac{2}{3}[/latex] [latex]x=sqrt{2}[/latex] lub [latex]x=-sqrt{2}[/latex] lub [latex]x=1frac{2}{3}[/latex] zad. 2 [latex](5x^2-25x+30)(-3x^2-6x+24)=0[/latex] [latex]5x^2-25x+30=0[/latex] lub [latex]-3x^2-6x+24=0[/latex] [latex]5x^2-25x+30=0[/latex] [latex]Delta = (-25)^2 - 4*5*30=625-600=25[/latex] [latex]x_1= frac{-(-25)-sqrt{25}}{2*5}=frac{25-5}{10}=frac{20}{10}=2[/latex] [latex]x_2 = frac{25+5}{10}=frac{30}{10}=3[/latex] [latex]-3x^2-6x+24=0[/latex] [latex]Delta=(-6)^2 - 4*(-3)*24=36+288=324[/latex] [latex]x_1=frac{-(-6)-sqrt{324}}{2*(-3)}=frac{6-18}{-6}=frac{-12}{-6}=2[/latex] [latex]x_2= frac{6+18}{-6}=frac{24}{-6}=-4[/latex] [latex]x=2[/latex] lub [latex]x=3[/latex] lub [latex]x=-4[/latex]