Question

Sabendo que p(x)=x3+(a+2)x2+(b-4)x-3 admite as raízes 1 e -1,o valor de a e b respectivamente é igual a

Answer 1

p(x)=x3+(a+2)x2+(b-4)x-3

p(1)=1+(a+2)+(b-4)-3=a+b-4=0

P(-1)=-1+a+2-b+4-3=a-b+2=0

a+b=4 (i)
a-b=-2 (ii)

(i)+(ii)

2a=2 ==>a=1

Usando a-b=-2 (ii)
1-b=-2
-b=-3
b=3