Question

qual o conjunto soluçao do polinomio P(x)=X³ - 10X² + 31X - 30 = 0 SABENDO QUE UMA DAS RAIZES E IGUAL A 2?

Answer 1

x^3-10x^2+31x-30= 0

briot ruffini

_2_|__1__-10__+31__-30_
___|__1__-8___15__-15

x^2-8x+15= 0

∆= b^2-4.a.c
∆= (-8)^2-4.1.(15)
∆= 64-60
∆= 4

x= -b+-√∆
__-----------
____2.a

x= -(-8)+-√4
___---------------
______2.1

x'= +8+2
__-------
____2

x'= 10/2

x'= 5

x"= +8-2
__----------
____2

x"= 6/2

x"= 3

S= {2,3,5}