Question

1. As raízes da equação: x² – 4x – 5 = 0 são: * a) – 1 e – 5
b) –1 e 5
c) 1 e 2
d) 1 e 5​

Answer 1

x² – 4x – 5 = 0

a = 1

b = -4

c=  -5

Δ = b² - 4ac

Δ = (-4)² - 4.1.(-5)

Δ = 16 + 20

Δ = 36

Usando bhaskara

x = -b ± √Δ /2a

x1 = 4 + 6 = 10 = 10/2 = 5

         2

x2 = 4 - 6 = -2/2 = -1

          2

S = { 5,-1}

Answer 2

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

uma equação do segundo grau

é representado por,

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

se trocarmos teremos os coeficientes

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

Agora temos que achar o valor de Delta ($\Delta$)

$\boxed{\begin{array}{lr} \Delta=b^2-4ac\\\Delta=(-4)^2-4.1.-5\\\Delta=16+20\\\Delta=36 \end{array}}$

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

Resposta Alternativa;

b) -1 e 5

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