Uma equação do do 3º grau pode ser escrita: ax³+bx²+cx+d=0, (a diferente de zero). Como deve ser escrita a equação polinomial cujas raízes são -1, 1 e 2?
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Boa noite!
Solução!
Por ser um polinômio do terceiro grau,admite três raízes.
![x_{1}=-1\\\\\
x_{2}=1\\\\\
x_{3}=2\\\\\\\\\
(x-x_{1})\times(x-x_{2})\times(x-x_{3})=0\\\\\\\\
(x-(-1))\times(x-1)\times(x-2)=0\\\\\\\\
(x+1)\times(x-1)\times(x-2)=0\\\\\\\\
( x^{2} -x+x-1)(\times(x-2)=0\\\\\\
( x^{2}-1)(\times(x-2)=0\\\\\\\
( x^{3} -2 x^{2} -x+2)=0\\\\\\\\\\\\
\boxed{Resposta:x^{3} -2 x^{2} -x+2=0}](https://tex.z-dn.net/?f=+x_%7B1%7D%3D-1%5C%5C%5C%5C%5C%0A+x_%7B2%7D%3D1%5C%5C%5C%5C%5C%0Ax_%7B3%7D%3D2%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%28x-x_%7B1%7D%29%5Ctimes%28x-x_%7B2%7D%29%5Ctimes%28x-x_%7B3%7D%29%3D0%5C%5C%5C%5C%5C%5C%5C%5C%0A%28x-%28-1%29%29%5Ctimes%28x-1%29%5Ctimes%28x-2%29%3D0%5C%5C%5C%5C%5C%5C%5C%5C%0A%28x%2B1%29%5Ctimes%28x-1%29%5Ctimes%28x-2%29%3D0%5C%5C%5C%5C%5C%5C%5C%5C%0A%28+x%5E%7B2%7D+-x%2Bx-1%29%28%5Ctimes%28x-2%29%3D0%5C%5C%5C%5C%5C%5C%0A%28+x%5E%7B2%7D-1%29%28%5Ctimes%28x-2%29%3D0%5C%5C%5C%5C%5C%5C%5C%0A%28+x%5E%7B3%7D+-2+x%5E%7B2%7D+-x%2B2%29%3D0%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3Ax%5E%7B3%7D+-2+x%5E%7B2%7D+-x%2B2%3D0%7D%0A "x_{1}=-1\\\\\
x_{2}=1\\\\\
x_{3}=2\\\\\\\\\
(x-x_{1})\times(x-x_{2})\times(x-x_{3})=0\\\\\\\\
(x-(-1))\times(x-1)\times(x-2)=0\\\\\\\\
(x+1)\times(x-1)\times(x-2)=0\\\\\\\\
( x^{2} -x+x-1)(\times(x-2)=0\\\\\\
( x^{2}-1)(\times(x-2)=0\\\\\\\
( x^{3} -2 x^{2} -x+2)=0\\\\\\\\\\\\
\boxed{Resposta:x^{3} -2 x^{2} -x+2=0}")
Boa noite!
Bons estudos!
Solução!
Por ser um polinômio do terceiro grau,admite três raízes.
Boa noite!
Bons estudos!
emayfair:
Muito obrigado!
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