Question

Calcule as raízes da equação 1x²+4x+3=0

Answer 1

As raizes da equação são, x'= -1 e x"= -3.

Aplicando a fórmula de Bháskara, temos:

$\Delta=b^2-4ac\\\\\Delta=4^2-4\cdot1\cdot3\\\\\Delta=16-12\\\\\Large\boxed{\Delta=4}\\\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\dfrac{-4\pm\sqrt{4}}{2\cdot1}\\\\\Large\boxed{x=\dfrac{-4\pm2}{2}}\\\\\\\boxed{\large\begin {array}{l}x'=\dfrac{-4+2}{2}\\\\x'=\dfrac{-2}{2}\\\\\Large\boxed{\boxed{x'=-1}}\Huge\checkmark\end {array}}\quad\quad\boxed{\large\begin {array}{l}x"=\dfrac{-4-2}{2}\\\\x"=\dfrac{-6}{2}\\\\\Large\boxed{\boxed{x"=-3}}\Huge\checkmark\end {array}}$

Portanto, as raizes são, x'=-1 e x"=-3.

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