Question

Determine os zeros da função quadrática: g(x) = - x² -3x -2 *

Answer 1

Função Quadrática

• Coeficientes:

$\boxed{ \begin{array}{lr} \large \sf \: a = - 1 \\\large \sf \: b = - 3 \\\large \sf \: c = - 2 \end{array}}$

• Cálculo Discriminante Delta:

$\boxed{ \begin{array}{lr} \\ \large \sf \: \Delta = {b}^{2} - 4ac \\ \\ \large \sf \Delta = {( - 3)}^{2} - 4 \cdot - 1 \cdot - 2 \\ \\ \large \sf\Delta = 9 - 8 \\ \\ \boxed{\large \sf \Delta = 1} \\ \: \end{array}}$

• Bhaskara:

$\boxed{ \begin{array}{lr} \large \sf \: x = \dfrac{ - b \: \pm \: \sqrt{\Delta} }{2.a} \\ \\ \\ \large \sf \: x = \dfrac{ - ( - 3) \: \pm \: \sqrt{1} }{2. - 1} \\ \\ \\ \large \sf \: x = \dfrac{ 3 \: \pm \: 1 }{ - 2} \\ \: \end{array}}$

• Raízes:

$\large \sf \: \boxed{ \boxed{ \large \sf \: x_{1} = \dfrac{ 3 + 1}{ - 2} = \red{- 2}}} \\ \\ \\ \large \sf \: \boxed{ \boxed{ \large \sf \: x_{2} = \dfrac{ 3 - 1}{ - 2} = \red{- 1}}}$

➡️ Resposta:

• $\huge \boxed{ \boxed{ \sf \: S = \{ - 1,- 2\}}}$