Question

Determine as raizes do polinomio de P(x)= x⁴-12x²+27

Answer 1

P(x) = x⁴-12x²+27

x² = y

P(x) = (x²)² - 12x² + 27
P(x) = y² - 12y + 27

y² - 12y + 27 = 0

a = 1
b = - 12
c = 27

Δ = b² - 4ac
Δ = (-12)² - 4.(1).(27)
Δ = 144 - 108
Δ = 36

$y = \dfrac{-b \frac{+}{-} \sqrt{b^2-4ac} }{2a}$

$y = \dfrac{-(-12) \frac{+}{-} \sqrt{36} }{2}$

$y = \dfrac{12 \frac{+}{-} 6 }{2}$

$y' = \dfrac{18 }{2}$

y' = 9

$y" = \dfrac{6}{2}$

y" = 3

x² = y
x = √y

x = √9
x' = 3
x" = -3

x"' = √3
x"" = -√3

S = {-3, -√3, √3, 3}