Question

resolva a equação do 2⁰ grua 3x²+5x-2=0 ​

Answer 1

$\bm\Large\begin{gathered} \begin{gathered}\large \overline{ \boxed{\boxed{ \begin{array}{r}\mathsf{ {3x}^{2} + 5x - 2 = 0 }\end{array}}}} \end{gathered}  \end{gathered}$

$\Large\mathsf\displaystyle{} \boxed{\begin{cases}a = 3 \\ b = 5 \\ c = - 2\end{cases}}$

$\Large\mathsf\displaystyle{}Formula: \boxed{x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }$

$\Large\mathsf\displaystyle{}x = \dfrac{ - 5 \pm \sqrt{ {5}^{2} - 4\cdot3\cdot\left( - 2\right) }}{2\cdot3}$

$\Large\mathsf\displaystyle{}x = \dfrac{ - 5 \pm \sqrt{25 + 24} }{6}$

$\Large\mathsf\displaystyle{}x = \dfrac{ - 5 \pm \sqrt{49} }{6}$

$\Large\mathsf\displaystyle{}x = \dfrac{ - 5 \pm7}{6}$

$\Large\mathsf\displaystyle{}x^\prime = \dfrac{ - 5 + 7 }{6}$

$\Large\mathsf\displaystyle{}x'' = \dfrac{ - 5 - 7}{6}$

Faça a expressão matemática das duas expressão matemática:

$\Large\mathsf\displaystyle{} x^\prime = \dfrac{1}{3}$

$\Large\mathsf\displaystyle{}x'' = - 2$

Então temos duas soluções:

$\bm\Large\begin{gathered} \begin{gathered}\large \overline{ \boxed{\boxed{ \begin{array}{r}\mathsf{ x_{1} = - 2, x_{2} = \dfrac{1}{3} }\end{array}}}} \end{gathered}  \end{gathered}$

$\bm\Large\begin{gathered} \begin{gathered}\large \overline{ \boxed{\boxed{ \begin{array}{r}\mathsf{\red{Bons~Estudos} }\end{array}}}} \end{gathered}  \end{gathered}$