Question

3) Quais são as raízes da equação " x² – 4x – 5 = 0"?
A) x'= 5 e x''= +1
B) x'= 10 e x''= +1
C) x'= -5 e x''= 2
D) x'= 5 e x''= -1​

Answer 1

$\boxed{\begin{array}{lr} x^2-4x-5=0 \end{array}}$

vou resolver utilizando a

fórmula de bhaskara

$\boxed{\begin{array}{lr} ax^2+bx+c=0 \end{array}}$

$\boxed{\begin{array}{lr} x^2-4x-5=0 \rightarrow\begin{cases} a=1\\b=-4\\c=-5\end{cases} \end{array}}$

Agora precisamos achar  o valor do discriminante

mais conhecido como Delta ($\Delta$)

$\Delta=b^2-4ac\\\Delta=(-4)^2-4.1.-5\\\Delta=16+20\\\Delta=36$

tendo o valor de delta

fica mais fácil para achar a raiz da equação.

$\boxed{\begin{array}{lr} x=\dfrac{4\pm6}{2} \end{array}}\\\boxed{\begin{array}{lr} x'=\dfrac{4+6}{2} \end{array}}\\\boxed{\begin{array}{lr} x'=\dfrac{10}{2} \end{array}}\\\boxed{\begin{array}{lr} x'=5 \end{array}}\\\boxed{\begin{array}{lr} x''=\dfrac{4-6}{2} \end{array}}\\\boxed{\begin{array}{lr} x''=\dfrac{-2}{2} \end{array}}\\\boxed{\begin{array}{lr} x''=-1 \end{array}}\\\\S=\{5,-1\}$

Resposta;

Alternativa;

d)

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