Question

2-Determine, se existirem, os zeros das funções abaixo: f(x) = x² – x – 2​

Answer 1

Resposta:

Explicação passo a passo:

Para achar os zeros faça f(x)=0

$\displaystyle Aplicando~a~f\acute{o}rmula~de~Bhaskara~para~x^{2}-x-2=0~~e~comparando~com~(a)x^{2}+(b)x+(c)=0,~determinamos~os~coeficientes:~\\a=1{;}~b=-1~e~c=-2\\\\C\acute{a}lculo~do~discriminante~(\Delta):&\\&~\Delta=(b)^{2}-4(a)(c)=(-1)^{2}-4(1)(-2)=1-(-8)=9\\\\C\acute{a}lculo~das~raizes:&\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-1)-\sqrt{9}}{2(1)}=\frac{1-3}{2}=\frac{-2}{2}=-1\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-1)+\sqrt{9}}{2(1)}=\frac{1+3}{2}=\frac{4}{2}=2\\\\S=\{-1,~2\}$

Answer 2

Resposta:

x = -1 e 2

Explicação passo a passo:

f(x) = x² – x – 2​

x² – x – 2​ = 0

x = (–b ± √(b² – 4 • a • c)) / (2 • a)

x = (–(– 1) ± √((– 1)² – 4 • 1 • (– 2))) / (2 • 1)

x = (1 ± √(1 – (– 8))) / 2

x = (1 ± √(1 + 8)) / 2

x = (1 ± √9) / 2

x = (1 ± √3²) / 2

x = (1 ± 3) / 2

x1 = (1 + 3) / 2

x1 = 4 / 2

x1 = 2

x2 = (1 - 3) / 2

x2 = - 2 / 2

x2 = - 1