Question

As raízes de uma equação do 2° grau são 1/3 e -1. Então a equação é:
COM CONTA
3x² – x – 1 = 0
3x² + x – 1 = 0
3x² + 2x – 1 = 0
3x² – 2x – 2 = 0
3x² – x + 1 = 0

Answer 1

Resposta:

OLÁ

VAMOS A SUA PERGUNTA:⇒⇒

$\sf3x^{2}+2x-1=0$

$\sf 3x^{2}+2x-1-\left(-1\right)=-\left(-1\right)$

$\sf3x^{2}+2x=-\left(-1\right)$

$\sf3x^{2}+2x=1$

$\sf\dfrac{3x^{2}+2x}{3}=\frac{1}{3}$

$\sf x^{2}+\dfrac{2}{3}x=\dfrac{1}{3}$

$\sf x^{2}+\dfrac{2}{3}x+\left(\dfrac{1}{3}\right)^{2}=\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^{2}$

$\sf x^{2}+\dfrac{2}{3}x+\dfrac{1}{9}=\dfrac{1}{3}+\dfrac{1}{9}$

$\sf\left(x+\dfrac{1}{3}\right)^{2}=\dfrac{4}{9}$

$\sf\sqrt{\left(x+\dfrac{1}{3}\right)^{2}}=\sqrt{\dfrac{4}{9}}$

$\sf x+\dfrac{1}{3}=\dfrac{2}{3} \\ x+\dfrac{1}{3}=-\dfrac{2}{3}$

$\boxed{\bold{\displaystyle{\clubsuit\ \spadesuit\ \maltese\ \sf \green{x=-1}}}}\ \checkmark \\\\\boxed{\bold{\displaystyle{\clubsuit\ \spadesuit\ \maltese\ \green{\dfrac{1}{3}\approx0.333333333} }}}\ \checkmark$←↑←↑ RESPOSTA.