(VALENDO 5 PONTOS)Resolva a equação do 2° grau.9*(2x-5)*(x+2) = 0.... Pergunta de ideia deExpertiee

January 2020 1 208 Report

(VALENDO 5 PONTOS)
Resolva a equação do 2° grau.

9*(2x-5)*(x+2) = 0

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$\large\begin{array}{l} \textsf{Resolver a equa\c{c}\~ao quadr\'atica}\\\\ \mathsf{9\cdot(2x-5)\cdot(x+2)=0}\\\\\\ \textsf{Dividindo os dois lados da equa\c{c}\~ao por 9,}\\\\ \mathsf{(2x-5)\cdot(x+2)=0} \end{array}$

$\large\begin{array}{l} \bullet~~\textsf{Forma 1:}\\\\\textsf{Quando que o produto de dois n\'umeros d\'a zero? Quando pelo}\\\textsf{menos um dos fatores \'e zero. Ent\~ao, devemos ter}\\\\ \begin{array}{rcl} \mathsf{2x-5=0}&~\textsf{ ou }~&\mathsf{x+2=0}\\\\ \mathsf{2x=5}&~\textsf{ ou }~&\mathsf{x=-2} \end{array}\\\\ \quad~\,\boxed{\begin{array}{c}\begin{array}{rcl} \mathsf{x=\dfrac{5}{2}}&~\textsf{ ou }~&\mathsf{x=-2} \end{array} \end{array}} \end{array}$

$\large\begin{array}{l} \textsf{Conjunto solu\c{c}\~ao: }\mathsf{S=\left\{\frac{5}{2},\,-2\right\}.} \end{array}$

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$\large\begin{array}{l} \bullet~~\textsf{Forma 2:}\\\\\textsf{Expandindo o produto e usando a f\'ormula de B\'ascara:}\\\\ \mathsf{(2x-5)\cdot(x+2)=0}\\\\ \mathsf{(2x-5)\cdot x+(2x-5)\cdot 2=0}\\\\ \mathsf{2x^2-5x+4x-10=0}\\\\ \mathsf{2x^2-x-10=0}\quad\Rightarrow\quad\left\{ \!\begin{array}{l} \mathsf{a=2}\\\mathsf{b=-1}\\\mathsf{c=-10} \end{array} \right. \end{array}$

$\large\begin{array}{l} \mathsf{\Delta=b^2-4ac}\\\\ \mathsf{\Delta=(-1)^2-4\cdot 2\cdot (-10)}\\\\ \mathsf{\Delta=1+80}\\\\ \mathsf{\Delta=81}\\\\ \mathsf{\Delta=9^2} \end{array}$

$\large\begin{array}{l} \mathsf{x=\dfrac{-b\pm \sqrt{\Delta}}{2a}}\\\\ \mathsf{x=\dfrac{-(-1)\pm \sqrt{9^2}}{2\cdot 2}}\\\\ \mathsf{x=\dfrac{1\pm 9}{4}}\\\\ \begin{array}{rcl} \mathsf{x=\dfrac{1-9}{4}}&~\textsf{ ou }~&\mathsf{x=\dfrac{1+9}{4}}\\\\ \mathsf{x=\dfrac{-8}{4}}&~\textsf{ ou }~&\mathsf{x=\dfrac{10}{4}} \end{array}\\\\ \quad\boxed{\begin{array}{rcl} \mathsf{x=-2}&~\textsf{ ou }~&\mathsf{x=\dfrac{5}{2}} \end{array}} \end{array}$

$\large\begin{array}{l} \textsf{Conjunto solu\c{c}\~ao: }\mathsf{S=\left\{\frac{5}{2},\,-2\right\}.} \end{array}$

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$\large\begin{array}{l} \textsf{D\'uvidas? Comente.}\\\\\\ \textsf{Bons estudos! :-)} \end{array}$

Expertiee Muito Obrigado!!!

Lukyo De nada =)

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