Wielomiany.
1. Rozwiąż równania:
a) ;
b) ;
c) .
a)b)c)
schemat Hornera
6x²+13x+13=0
Δ=13²-4*6*13
Δ=169-312
Δ=-143 ⇒ brak rozwiązania
x=1
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a)![\\(x^{2}+8x+12)(x^{2}+6x-7)=0\\ (x^2+2x+6x+12)(x^2-x+7x-7)=0\\ (x(x+2)+6(x+2))(x(x-1)+7(x-1))=0\\ (x+6)(x+2)(x+7)(x-1)=0\\ x=-6 \vee x=-2 \vee x=-7 \vee x=1 \\(x^{2}+8x+12)(x^{2}+6x-7)=0\\ (x^2+2x+6x+12)(x^2-x+7x-7)=0\\ (x(x+2)+6(x+2))(x(x-1)+7(x-1))=0\\ (x+6)(x+2)(x+7)(x-1)=0\\ x=-6 \vee x=-2 \vee x=-7 \vee x=1](https://tex.z-dn.net/?f=%5C%5C%28x%5E%7B2%7D%2B8x%2B12%29%28x%5E%7B2%7D%2B6x-7%29%3D0%5C%5C+%28x%5E2%2B2x%2B6x%2B12%29%28x%5E2-x%2B7x-7%29%3D0%5C%5C+%28x%28x%2B2%29%2B6%28x%2B2%29%29%28x%28x-1%29%2B7%28x-1%29%29%3D0%5C%5C+%28x%2B6%29%28x%2B2%29%28x%2B7%29%28x-1%29%3D0%5C%5C+x%3D-6+%5Cvee+x%3D-2+%5Cvee+x%3D-7+%5Cvee+x%3D1)
![\\x^{3}-3x^{2}+x-3=0\\ x^2(x-3)+1(x-3)=0\\ (x^2+1)(x-3)=0\\ x=3 \\x^{3}-3x^{2}+x-3=0\\ x^2(x-3)+1(x-3)=0\\ (x^2+1)(x-3)=0\\ x=3](https://tex.z-dn.net/?f=%5C%5Cx%5E%7B3%7D-3x%5E%7B2%7D%2Bx-3%3D0%5C%5C+x%5E2%28x-3%29%2B1%28x-3%29%3D0%5C%5C+%28x%5E2%2B1%29%28x-3%29%3D0%5C%5C+x%3D3)
b)
c)
schemat Hornera
6x²+13x+13=0
Δ=13²-4*6*13
Δ=169-312
Δ=-143 ⇒ brak rozwiązania
x=1