Question

7x²+2x-5=0

fórmula de bhaskara

Answer 1

$\Large\displaystyle\text{ \begin{gathered} \tt(I)\,\blue{\sf{ Coeficientes\,e\, delta:}} \end{gathered} }$

$\Large\displaystyle\begin{gathered} \sf{7x^2+2x-5=0 } \end{gathered}$

$\Large\displaystyle\text{ \begin{gathered} \sf{\begin{cases}\sf a=7\\\sf b=2\\\sf c=-5\end{cases} } \end{gathered} }$

$\Large\displaystyle\begin{gathered} \sf{\Delta=b^2-4ac } \end{gathered}$

$\Large\displaystyle\begin{gathered} \sf{ \Delta=2^2-4\cdot7\cdot(-5)} \end{gathered}$

$\Large\displaystyle\begin{gathered} \sf{ \Delta=4+140} \end{gathered}$

$\Large\displaystyle\begin{gathered} \sf{ \Delta=144} \end{gathered}$

$\Large\displaystyle\text{ \begin{gathered} \tt(II)\,\blue{\sf{Ra\acute{i}zes:} } \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ x=\frac{-b\pm\sqrt{\Delta}}{2a}} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{x=\frac{-2\pm\sqrt{144}}{2\cdot7} } \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \sf{ x=\frac{-2\pm12}{14}\begin{cases}\sf x_1=\dfrac{-2+12}{14}=\dfrac{10\div2}{14\div2}=\dfrac{5}{7}\\\\\sf x_2=\dfrac{-2-12}{14}=\dfrac{-14}{14}=-1\end{cases}} \end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \tt(III)\,\blue{\sf{ Conjunto\, soluc_{\!\!,}\tilde{a}o:} }\end{gathered} }$

$\Large\displaystyle\text{ \begin{gathered} \therefore\green{\underline{\boxed{\boxed{\sf{ S=\bigg\{\frac{5}{7},-1\bigg\}}}}}} ~~(\checkmark)\end{gathered} }$