Question

10- a) 6
b) -6
c) 5
d) -5​

Answer 1

Explicação passo-a-passo:

9) Determinar as raízes da equação:

$\mathsf{x^2 - 2x - 8 = 0}$

$\mathsf{a = 1~~b = - 2~~ c = - 8}$

$\mathsf{\Delta = b^2 - 4ac}$

$\mathsf{\Delta = (-2)^2 - 4\cdot1\cdot(-8)}$

$\mathsf{\Delta = 4 + 32}$

$\mathsf{\Delta = 36}$

$\mathsf{x = \dfrac{- b \pm \sqrt{\Delta}}{2a}}$

$\mathsf{x = \dfrac{- (-2) \pm \sqrt{36}}{2\cdot1}}$

$\mathsf{x = \dfrac{2 \pm 6}{2}}$

$\mathsf{\star \: x' = \dfrac{2 + 6}{2} = \dfrac{8}{2} = 4}$

$\mathsf{\star \: x" = \dfrac{2 - 6}{2} = - \dfrac{4}{2} = - 2}$

$\boxed{\mathsf{S = \left\{- 2 \: \: ; \: \: 4 \: \right\}}}$

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10) Determinar as raízes da equação:

$\mathsf{x^2 + 12x + 36 = 0}$

$\mathsf{a = 1~~b = 12~~c = 36}$

$\mathsf{\Delta = b^2 - 4ac}$

$\mathsf{\Delta = {12}^2 - 4\cdot1\cdot36}$

$\mathsf{\Delta = 144 - 144}$

$\mathsf{\Delta = 0}$

$\mathsf{x = \dfrac{- b \pm \sqrt{\Delta}}{2a}}$

$\mathsf{x = \dfrac{- 12 \pm \sqrt{0}}{2\cdot1}}$

$\mathsf{x = \dfrac{- 12 \pm 0}{2}}$

$\mathsf{x = - \dfrac{12}{2} = - 6}$

$\boxed{\mathsf{S = \left\{- 6 \right\}}}$