Question

Resolva a equação x2-x-42=0​

Answer 1

Resposta:

$\sf x^{2} -x - 42 = 0$

$\sf ax^{2} + bx +c = 0$

a = 1

b = - 1

c = - 4 2

Determinar o Δ:

$\sf \Delta = b^2 -\:4ac$

$\sf \Delta = ( - 1)^2 -\:4 \cdot 1 \cdot ( - 42)$

$\sf \Delta = 1 + 168$

$\sf \Delta = 169$

Determinar as raízes da equação:

$\sf x = \dfrac{-\,b \pm \sqrt{ \Delta } }{2a} = \dfrac{ 1 \pm \sqrt{ 169 } }{2\cdot 1} = \dfrac{1 \pm 13 }{2} \Rightarrow\begin{cases} \sf x_1 = &\sf \dfrac{1 + 13}{2} = \dfrac{14}{2} = \:7 \\\\ \sf x_2 = &\sf \dfrac{1 - 13}{2} = \dfrac{- 12}{2} = - 6\end{cases}$

$\sf \boldsymbol{ \sf \displaystyle S = \{ x \in \mathbb{R} \mid x = -\: 6 \mbox{\sf \;e } x = 7 \} }$