Question

MATEMÁTICA
01 - Na equação abaixo, calcule as raízes e marque a
resposta correta
x2= x + 12

( ) (-3,-4)
( ) (-2,-4)
( ) (-3,4)
( ) (0,6)
( ) (-2,7)​

Answer 1

Resposta:

S={-3, 4}

Explicação passo-a-passo:

x²=x+12

x²-x-12=0

$\displaystyle Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-x-12=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=1{;}~b=-1~e~c=-12\\\\C\'alculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(-1)^{2}-4(1)(-12)=1-(-48)=49\\\\C\'alculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-1)-\sqrt{49}}{2(1)}=\frac{1-7}{2}=\frac{-6}{2}=-3\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-1)+\sqrt{49}}{2(1)}=\frac{1+7}{2}=\frac{8}{2}=4\\\\S=\{-3,~4\}$