Question

Encontre as raízes da equação:×2-4×-5=0

Answer 1

As raízes da equação de 2º grau são, x'= 5 e x" = -1.

• Aplicando a fórmula de Bháskara, temos:

$\Delta=b^2-4ac\\\\\Delta=(-4)^2-4\cdot1\cdot(-5)\\\\\Delta=16+20\\\\\Large\boxed{\Delta=36}\\\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\dfrac{-(-4)\pm\sqrt{36}}{2\cdot1}\\\\\Large\boxed{x=\dfrac{4\pm6}{2}}\\\\\\\boxed{\large\begin {array}{l}x'=\dfrac{4+6}{2}\\\\x'=\dfrac{10}{2}\\\\\Large\boxed{\boxed{x'=5}}\Huge\checkmark\end {array}}\quad\quad\boxed{\large\begin {array}{l}x"=\dfrac{4-6}{2}\\\\x"=\dfrac{-2}{2}\\\\\Large\boxed{\boxed{x"=-1}}\Huge\checkmark\end {array}}$

Portanto, as raízes da equação de 2º grau é x'= 5 e x" = -1.

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Bons estudos!