Find the values of a and b given that the polynomial P(x) = x^3+ ax^2 +x+b, is divisible by both x1 and x + 3.
Mathematics
miraismail2909
Question
Find the values of a and b given that the polynomial P(x) = x^3+ ax^2 +x+b, is divisible by
both x1 and x + 3.
both x1 and x + 3.
1 Answer

1. User Answers freckledspots
Answer:
a=4
b=6
Stepbystep explanation:
If P(x) is divisible by xc, then P(c)=0.
So P(1)=0 implies 1^3+a1^2+1+b=0
and
P(3)=0 implies (3)^2+a(3)^2+3+b=0
So notice we have a system to solve.
Let's simply it.
First equation:
1^3+a1^2+1+b=0
1+a+1+b=0
2+a+b=0
a+b=2
Second equation:
(3)^3+a(3)^2+3+b=0
27+9a3+b=0
9a+b30=0
9a+b=30
Let's put our system together:
a+b=2
9a+b=30
This is setup so if we subtract the equations b will eliminate allowing us to solve for a:
8a=32
a=4
If a=4 and a+b=2, then 4+b=2 giving us b=6.
a=4
b=6