Resposta:
4x² - 2x + 1 = 0
∆ = b² - 4ac
∆ = (-2)² - 4 . 4 . 1
∆ = 4 - 16
∆ = -12
Delta negativo, não existem raízes reais.
Resolução no universo dos complexos
x = (-b ± √∆) / 2a
x = [-(-2) ± √(-12)] / (2 .4)
x = (2 ± √12 . √(-1)) / 8
x = (2 ± √(2² . 3) . i) / 8
x = (2 ± 2√3i) / 8
x = 2 . (1 ± √3i) / 8
x = (1 ± √3i) / 4
x' = (1 - √3i) / 4
x'' = (1 + √3i) / 4
Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo-a-passo:
[tex]\mathsf{1\ª\:solu{\c c}{\~ao}}[/tex]
[tex]\mathsf{4x^2 - 2x = 0}[/tex]
[tex]\mathsf{x(4x - 2) = 0}[/tex]
[tex]\mathsf{x = 0}[/tex]
[tex]\mathsf{4x - 2 = 0}[/tex]
[tex]\mathsf{4x = 2}[/tex]
[tex]\mathsf{x = \dfrac{1}{2}}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \{0;\dfrac{1}{2}\}}}}\leftarrow\textsf{duas ra{\'i}zes reais}[/tex]
[tex]\mathsf{2\ª\:solu{\c c}{\~ao}}[/tex]
[tex]\mathsf{4x^2 - 2x = 0}\rightarrow\begin{cases}\mathsf{a = 4}\\\mathsf{b = -2}\\\mathsf{c = 0}\end{cases}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = (-2)^2 - 4.4.0}[/tex]
[tex]\mathsf{\Delta = 4 - 0}[/tex]
[tex]\mathsf{\Delta = 4}[/tex]
[tex]\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{2 \pm \sqrt{4}}{8} \rightarrow \begin{cases}\mathsf{x' = \dfrac{2 + 2}{8} = \dfrac{4}{8} = \dfrac{1}{2}}\\\\\mathsf{x'' = \dfrac{2 - 2}{8} = \dfrac{0}{8} = 0}\end{cases}}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \{0;\dfrac{1}{2}\}}}}\leftarrow\textsf{duas ra{\'i}zes reais}[/tex]
