Rozwiąż równania wielomianowe: x^3 - 9x^2 + 23x - 15= 0 x^4 + x^3 - 14x^2 + 26x - 20=0 5x^5 + 4x^4 - 5x - 4 = 0

  [latex]x^3 -9x^2 + 23x - 15 = 0\ x^3 - x^2 -8x^2 + 8x + 15x - 15 = 0\ x^2(x-1) -8x(x-1) + 15(x-1) = 0\ (x-1)(x^2 -8x + 15) = 0\ x-1=0\ x=1\ x^2 -8x + 15 = 0\ Delta= 64 - 60 = 4\ x=frac{8-2}{2} = 3\ x=frac{8+2}{2} = 5[/latex]     [latex]x^4 + x^3 - 14x^2 + 26x - 20=0\ x^4 - 2x^3 + 3x^3 - 6x^2 - 8x^2 + 16x +10x - 20 =0\ x^3(x-2) + 3x^2(x-2) - 8x(x-2) + 10(x-2) = 0\ (x-2)(x^3 + 3x^2 - 8x +10) = 0\ x-2=0\ x=2\ x^3 + 3x^2 - 8x +10 = 0\ x^3 + 5x^2 -2x^2 -10x + 2x +10 = 0\ x^2(x+5) -2x(x+5) +2(x+5) =0\ (x+5)(x^2-2x+2) =0\ x+5=0\ x=-5\ x^2-2x+2=0\ Delta=4-8-4 <0[/latex]   [latex] 5x^5 + 4x^4 - 5x - 4 = 0 \ x^4(5x+4) -1(5x+4) = 0\ (5x+4)(x^4-1) =0\ 5x+4=0\ 5x=-4\ x=-frac{4}{5}\ x^4 -1=0\ x^4=1\ x=1\ x=-1[/latex]