Question

Determine a solução da equação x² – x – 12 = 0 (por favor, não sei como montar a conta juntoda fórmula de delta)

Answer 1

$\large\displaystyle\text{ \mathsf{ x {}^{2} - x - 12 = 0 } }$

$\large\displaystyle\text{ \mathsf{ \begin{cases} \sf a = 1 \\ \sf b = - 1 \\ \sf c = - 12\end{cases}} }$

$\large\displaystyle \mathsf{\Delta=b^2-4ac }$

$\large\displaystyle \mathsf{\Delta=(-1)^2-4\cdot1\cdot(-12) }$

$\large\displaystyle \mathsf{\Delta=1+48 }$

$\large\displaystyle \mathsf{ \Delta=49 }$

$\large\displaystyle\text{ \mathsf{ x=\dfrac{-b\pm\sqrt{\Delta}}{2a}} }$

$\large\displaystyle\text{ \mathsf{ x = \dfrac{ - ( - 1) \pm \sqrt{49} }{2 \cdot{1}} } }$

$\large\displaystyle\text{ \mathsf{ x = \dfrac{1 \pm7}{2} \begin{cases} \sf x _{1} = \dfrac{1 + 7}{2} = \dfrac{8}{2} = 4 \\ \\ \sf x _{2} = \dfrac{1 - 7}{2} = \dfrac{ - 6}{2} = - 3\end{cases} } }$

$\large\displaystyle\text{ \boxed{\boxed{\mathsf{ S=\{-3;4\}}}} }$