1) w(x) = 5x³ + 10x² + 5x = 5x(x² + 2x + 1) = 5x(x + 1)² 2) w(x) = 0 2x⁵ - 14x⁴ + 20x³ = 0 2x³(x² - 7x + 10) = 0 2x³(x² - 2x - 5x + 10) = 0 2x³ [x(x - 2) - 5(x - 2)] = 0 2x³ (x - 5)(x - 2) = 0 x = 0 lub x = 5 lub x = 2
zadanie 1 [latex]W(x)=5x^{3}+10x^{2}+5x\W(x)=5x(x^{2}+2x+1) o Wzor: a^{2}+2ab+b^{2}=(a+b)^{2}\underline{underline{W(x)=5x(x+1)^{2}}}[/latex] zadanie 2 Rozkładamy wielomian na czynniki: [latex]W(x)=2x^{5}-14x^{4}+20x^{3}\W(x)=2x^{3}(x^{2}-7x+10)\\x^{2}-7x+10=0\Delta=b^{2}-4ac=(-7)^{2}-4*1*10=49-40=9\sqrt{Delta}=3\x_{1}=frac{-b-sqrt{Delta}}{2a}=frac{7-3}{2}=frac{4}{2}=2\\x_{2}=frac{-b+sqrt{Delta}}{2a}=frac{7+3}{2}=frac{10}{2}=5\\x^{2}-7x+10=(x-2)(x-5)\\underline{underline{W(x)=2x^{3}(x-2)(x-5)}} [/latex] Rozwiązujemy równanie: [latex]W(x)=2x^{3}(x-2)(x-5)\\W(x)=0\2x^{3}(x-2)(x-5)=0\2x^{3}=0 lub x-2=0 lub x-5=0\x^{3}=0 x=2 x=5\x=0\\x in {0; 2; 5}[/latex]
