Question

Considere a equação de segundo grau Y= x² + 5x + 6. As raizes dessa equação são:

Answer 1

As raízes da equação de 2º grau, são: x'= -2 e x"= -3.

Acompanhe a solução:

Sendo Y=0, aplicando a fórmula de Bháskara, temos:

Cálculo:

$Y=x^2+5x+6\\\\\Large\boxed{0=x^2+5x+6}\\\\\\\Delta=b^2-4ac\\\\\Delta=5^5-4\cdot1\cdot6\\\\\Delta=25-24\\\\\boxed{\Delta=1}\\\\\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\dfrac{-5\pm\sqrt{1}}{2\cdot1}\\\\\boxed{x=\dfrac{-5\pm1}{2}}$

$\boxed{\large\begin {array}{l}x'=\dfrac{-5+1}{2}\\\\x'=\dfrac{-4}{2}\\\\\Large\boxed{\boxed{x'=-2}}\Huge\checkmark\end {array}} \quad\quad \boxed{\large\begin {array}{l}x"=\dfrac{-5-1}{2}\\\\x"=\dfrac{-6}{2}\\\\\Large\boxed{\boxed{x"=-3}}\Huge\checkmark\end {array}}$

Resposta:

Portanto, as raízes da equação de 2º grau, são: x'= -2 e x"= -3.

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Bons estudos!