Zad 1. a) [latex]x^2-4x+3=0\delta=16-4*3*1=16-12=4\sqrt{delta}=2\x_{1}=frac{4-2}{2}=1\x_{2}=frac{4+2}{2}=3[/latex] b) [latex]x^2-6x+5=0\delta=36-4*5*1=36-20=16\sqrt{delta}=4\x_{1}=frac{6-4}{2}=1\x_{2}=frac{6+4}{2}=5[/latex] c) [latex]9x^2-30x+25=0\delta=900-4*25*9=900-900=0\x_{0}=frac{30}{18}=1frac{12}{18}=1frac{2}{3}[/latex] d) [latex]6x^2+7x-3=0\delta=49-4*6*(-3)=49+72=121\sqrt{delta}=11\x_{1}=frac{-7-11}{12}=-frac{18}{12}=-1,5\x_{2}=frac{-7+11}{12}=frac{4}{12}=frac{1}{3}[/latex] Zad 2. a) [latex]x^3+2x^2+4x-8=0\(x^3+2x^2)+(4x-8)=0\x^2(x+2)+4(-x-2)=0\x^2(x+2)-4(x+2)=0\(x^2-4)(x+2)=0\x^2-4=0 x+2=0\(x+2)(x-2)=0 x= -2\x= -2 x=2[/latex] b) [latex]8x^4+24x^3-x-3=0\(8x^4+24x^3)+(-x-3)=0\8x^3(x+3)-1(x+3)=0\(8x^3-1)(x+3)=0[/latex] 8x³-1=0 x+3=0 8x³=1 |:8 x= -3 x³ = ⅛ |∛ x = ½
