Question

2) Calcule as raízes da seguinte equação: x² + 2x – 24 = 0. * A) x’ = 4 e x” = - 6 B) x’ = - 1 e x” = 2 C) x’ = 5 e x” = 11 D) x’ = 4 e x” = - 1 E) x’ = - 6 e x” = - 2

Answer 1

As raízes da equação de 2º grau, são: x'= 4 e x"= -6. Alternativa A!

Acompanhe a solução:

Aplicando a fórmula de Bháskara, temos:

Cálculo:

$\Delta=b^2-4ac\\\\\Delta=2^2-4\cdot1\cdot(-24)\\\\\Delta=4+96\\\\\Large\boxed{\Delta=100}\\\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\dfrac{-2\pm\sqrt{100}}{2\cdot1}\\\\\Large\boxed{x=\dfrac{-2\pm10}{2}}\\\\\\\boxed{\large\begin {array}{l}x'=\dfrac{-2+10}{2}\\\\x'=\dfrac{8}{2}\\\\\Large\boxed{\boxed{x'=4}}\Huge\checkmark\end {array}}\quad\quad\boxed{\large\begin {array}{l}x"=\dfrac{-2-10}{2}\\\\x"=\dfrac{-12}{2}\\\\\Large\boxed{\boxed{x"=-6}}\Huge\checkmark\end {array}}$

Resposta:

Portanto, as raízes, são? x'=4 e x"= -6. Alternativa A!

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Bons estudos!