Question

Equação do segundo grau 3x elevado a 2 + 5x + 1 = 0.

Answer 1

A Raiz da Equação é; x=-5±√13/6

• Para achar a raiz, é preciso ter seus coeficientes e calcular o Discriminante, Mais conhecido como Delta.

$\boxed{\begin{array}{lr} a=3\\b=5\\c=1 \end{array}}\\\\\boxed{\begin{array}{lr} \Delta=b^2-4.a.c\\\Delta=5^2-4.3.1\\\Delta=25-12\\\Delta=13\ \ \checkmark \end{array}}$

• Agora que já temos o Delta basta resolver.

$\boxed{\begin{array}{lr} x=\dfrac{-b\pm\sqrt{13}}{2.3} \end{array}}\to\boxed{\begin{array}{lr} x=\dfrac{-5\pm\sqrt{13}}{6} \end{array}}\\\\\\\boxed{\begin{array}{lr} \boxed{\begin{array}{lr} x'=\dfrac{-5+\sqrt{13}}{6} \end{array}}\ \\ \\ \ \ \ \ \ \ \ \ \ \ \checkmark\\\\\boxed{\begin{array}{lr} x''=\dfrac{-5-\sqrt{13}}{6} \end{array}} \end{array}}$

Resposta;

x=-5±√13/6

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