Question

encontre as raisez x⁴-x²-12=0

Answer 1

$x^{4}-x^{2}-12=0\\\\ fazendo\,\,u = x^{2}\\\\ u^{2}-u-12=0$

$\Delta = (-1)^{2}-4.1.(-12)\\ \Delta = 49\\\\ u' = \frac{-(-1) + 7}{ 2.1} \,\,e\,\, u'' = \frac{-(-1) - 7}{ 2.1}\\\\ u' = 4\,\,e\,\,u''=-3$

Substituindo de volta,

x² = 4 ⇒ √4 e -√4 ∴ x = 2  e x = -2
x² = -3 ⇒ x = √-3 e -√-3 ∴ x = √3i e x = -√3i

Assim, as raízes são x = 2, x = -2, x = √3i e x = -√3i