Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\mathsf{L(x) = 100.(10 - x).(x - 2)}[/tex]
[tex]\mathsf{L(x) = 100.(10x - 20 -x^2 + 2x)}[/tex]
[tex]\mathsf{L(x) = 100.(-x^2 + 12x - 20)}[/tex]
[tex]\mathsf{L(x) = -100x^2 + 1.200x - 2.000}[/tex]
[tex]\mathsf{\dfrac{12.000}{10} = -100x^2 + 1.200x - 2.000}[/tex]
[tex]\mathsf{-100x^2 + 1.200x - 3.200 = 0}[/tex]
[tex]\mathsf{\Delta = b^2 - 4.a.c}[/tex]
[tex]\mathsf{\Delta = (1.200)^2 - 4.(-100).(-3.200)}[/tex]
[tex]\mathsf{\Delta = 1.440.000 - 1.280.000}[/tex]
[tex]\mathsf{\Delta = 160.000}[/tex]
[tex]\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{-1.200 \pm \sqrt{160.000}}{-200} \rightarrow \begin{cases}\mathsf{x' = \dfrac{-1.200 + 400}{-200} = \dfrac{-800}{-200} = 4}\\\\\mathsf{x'' = \dfrac{-1.200 - 400}{-200} = \dfrac{-1.600}{-200} = 8}\end{cases}}[/tex]
[tex]\boxed{\boxed{\mathsf{S = \{4;8\}}}}\leftarrow\textsf{letra B}[/tex]
