Question

Dentre os números -2, 0, 1, 4, quais deles são raízes da equação x² – 2x - 8 = 0?

-2 e 0

-2 e 4

1 e 4

0 e 1
​

Answer 1

Resposta:

Explicação passo a passo:

$\displaystyle Aplicando~a~f\acute{o}rmula~de~Bhaskara~para~x^{2}-2x-8=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=1{;}~b=-2~e~c=-8\\\\C\acute{a}lculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(-2)^{2}-4(1)(-8)=4-(-32)=36\\\\C\acute{a}lculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-2)-\sqrt{36}}{2(1)}=\frac{2-6}{2}=\frac{-4}{2}=-2\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-2)+\sqrt{36}}{2(1)}=\frac{2+6}{2}=\frac{8}{2}=4\\\\S=\{-2,~4\}$