a) [latex] x^5 + x ^4 +4x^3+ 8x^2 +8x +32=0\(x^5+x^4+4x^3)+(8x^2+8x+32)=0\x^3(x^2+x+4)+8(x^2+x+4)=0\(x+2)^2(x^3+8)=0[/latex] x+2≠0 x³+8≠0 x≠ -2 x∈Ф b) [latex]x^5 - 2x^4 +3x^3-27x^2+54x-81=0\(x^5-2x^4+3x^3)+(-27x^2+54x-81)=0\x^3(x^2-2x+3)-27(x^2-2x+3)=0\(x^3-27)(x^2-2x+3)=0[/latex] x³-27≠0 x³≠27 x≠3 ∨ x≠ -3 x²-2x+3≠0 delta <0 więc brak pierwiastków. x∈Ф c) [latex]8x^5+32x^4+24x^3-x^2-4x-3=0\ (8x^5+32x^4+24x^3)+(-x^2-4x-3)=0\8x^3(x^2+4x+3)-1(x^2+4x+3)=0\(8x^3-1)(x^2+4x+3)=0[/latex] 8x³-1≠0 |:8 x³≠⅛ |∛ x≠½ x^2+4x+3≠0 Δ= 16-4*3*1=16-12=4 √Δ=2 x₁= (4-2):2=1 x₂= (4+2):2=3 czyli (x-1)(x-3)≠0 x≠ 1 ∧ x≠ 3 d) [latex]x^5+2x^4 +x^3 +x^2 +2x+1=0\(x^5+2x^4+x^3)+(x^2+2x+1)=0\x^3(x^2+2x+1)+1(x^2+2x+1)=0\(x^3+1)(x+1)^2=0[/latex] x³+1≠0 (x+1)^2≠0 |√ x³≠ -1 x+1≠0 x≠ -1 x≠ -1 e)[latex]x^4-2x^3-8x+16=0\(x^4-2x^3)+(-8x+16)=0\x^3(x-2)-8(x-2)=0\(x^3-8)(x-2)=0[/latex] x³-8≠0 x-2≠0 x³≠ 8 x≠ 2 x≠ 2 f)[latex]x^4+3x^3+27x+81=0\x^3(x+3)+27(x+3)=0\(x^3+27)(x+3)=0[/latex] x³+27≠0 x+3≠0 x³≠ -27 x≠ -3 x ≠ -3 g) [latex]x^4-x^3+8x-8=0\x^3(x-1)+8(x-1)=0\(x^3+8)(x-1)=0[/latex] x³+8≠0 x-1≠0 x³≠ -8 x≠ 1 x≠ -2 h) [latex]-x^4-4x^3+x+4=0\(-x^4-4x^3)+(x+4)=0\-x^3(x+4)+1(x+4)=0\(-x^3+1)(x+4)=0[/latex] -x³+1≠0 x+4≠0 -x³ ≠ -1 |*(-1) x≠ -4 x³ ≠ 1 x ≠ 1 * Ф - jest to zbiór pusty w moim rozwiązaniu. Pozdrawiam :)
