Question

Encontre as raízes da função f (x) = -2x² + 4.x – 9​

Answer 1

Explicação:

$\sf -2x^2+4x-9=0$

$\sf \Delta=4^2-4\cdot(-2)\cdot(-9)$

$\sf \Delta=16-72$

$\sf \Delta=-56$

Não há raízes reais

Nos complexos:

$\sf \Delta=56\cdot(-1)$

$\sf \Delta=56i^2$

$\sf x=\dfrac{-4\pm\sqrt{56i^2}}{2\cdot(-2)}=\dfrac{-4\pm2i\sqrt{14}}{-4}$

$\sf x'=\dfrac{-4+2i\sqrt{14}}{-4}~\Rightarrow~\red{x'=1-\dfrac{i\sqrt{14}}{2}}$

$\sf x"=\dfrac{-4-2i\sqrt{14}}{-4}~\Rightarrow~\red{x"=1+\dfrac{i\sqrt{14}}{2}}$

Answer 2

Resposta:

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