Question

quais são as raízes da função -3x2+6x+9

Answer 1

Equação do segundo grau

$- 3 {x}^{2} + 6x + 9 = 0 \\ ( - 3x {}^{2} + 6x + 9) \div ( - 3) =0$

Faça a distributiva

$\underbrace{{(  - 3 {x}^{2} + 6x + 9 } { ) }} \div ( - 3) = 0 \\ _{  x {}^{2} - \: 2x \: - \: 3 \: = \: 0 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

${x}^{2} - 2x - 3 = 0\begin{gathered}\begin{cases} {a = 1}\\{b - 2} \\ c = - 3\end{cases}\end{gathered} \\ Δ = {b}^{2} - 4.a.c \\ Δ = ( - 2 {)}^{2} - 4 \times 1 \times ( - 3) \\ Δ = 4 + 12 \\ Δ = 16 \\ x = \frac{ - b± \sqrt{Δ} }{2.a} \\ \\ x = \frac{ - ( - 2)± \sqrt{16} }{2 \times 1} \\ \\ x = \frac{2±4}{2} \begin{gathered}\begin{cases} { \frac{2 + 4}{2} } = \frac{6}{2} = 3\\{ \frac{2 - 4}{2} } = \frac{ - 2}{2} = - 1 \end{cases}\end{gathered} \\ \color{green}S = [x_{1} = - 1 \: ,x_{2} = 3]$

$\mathcal{Bons \: estudos }$

$\displaystyle\int_ \empty ^ \mathbb{C}     \frac{ - b \: ± \:  \sqrt{ {b}^{2} - 4 \times a \times c } }{2 \times a} d{ t } \boxed{ \boxed{ \mathbb{\displaystyle\Re}\sf{ \gamma  \alpha }\tt{ \pi}\bf{ \nabla}}}$