Question

O conjunto solução da equação: - x² + x + 12 = 0 é: *

( ) a) S ={ }

( ) b) S = { 3 , 4}

( ) c) S = { -3 , 4}

( ) d) S = { -4 , -3}

( ) e) S = { -4 , 3}​

Answer 1

Resposta:

Alternativa C.

$\boxed{\bf{S=\{-3, 4\}}}$

Explicação passo-a-passo:

Vamos resolver o exercício pela fórmula resolutiva:

- x² + x + 12 = 0 (× -1)

x² - x - 12 = 0

a = 1; b = -1; c = -12

$x=\dfrac{-b\pm\sqrt{b^2 - 4\times a\times c}}{2\times a}\\\\x=\dfrac{-(-1)\pm\sqrt{(-1)^2 - 4\times 1\times (-12)}}{2\times 1}\\\\x=\dfrac{+1\pm\sqrt{1 + 48}}{2}=\dfrac{1\pm\sqrt{49}}{2}=\dfrac{1\pm7}{2}\\\\x_1=\dfrac{1+7}{2}=\dfrac{8}{2}=4\\\\\boxed{\bf{x_1=4}}\\\\x_2=\dfrac{1-7}{2}=\dfrac{-6}{2}=-3\\\\\boxed{\bf{x_2=-3}}\\\\\\\boxed{\bf{S=\{-3, 4\}}}$

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