Question

Encontre as raízes de P(x)=x^3+3x-4

Answer 1

x³+3x-4 = x³-1 + 3x-3
= (x-1)(x²+x+1) + 3.(x-1)
= (x-1)(x²+x+1+3)
= (x-1)(x²+x+4)

Agora analisamos as raízes dos dois fatores :

x-1 —› raíz 1

x²+x+4
∆ = 1²-4.1.4 = 1-16 = -15

x = (-1±√-15 )/2
x = -1/2 ± i.√15/2