Find all zeros of the polynomial. P(x)=x^{5}+x^{3}+8x^{2}+8

Anne Wacker 2021-12-14 Answered
Find all zeros of the polynomial.
P(x)=x5+x3+8x2+8
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Expert Answer

reinosodairyshm
Answered 2021-12-15 Author has 36 answers
Step 1
Consider the given polynomial as
p(x)=x5+x3+8x2+8
Step 2
Simplify as
x5+x3+8x2+8=x3(x2+1)+1(x2+1)
=(x3+1)(x2+1)
For find zero above factor set up to equal to zero.
(x3+1)(x2+1)=0
x3+1=0
x=-1
And
x2+1=0
x2=1
Square can not be negative.

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Cleveland Walters
Answered 2021-12-16 Author has 40 answers
The given polynomial P(x)=x5+x3+8x2+8
We first factor P as follows
P(x)=x5+x3+8x2+8
=x3(x2+1)+8(x2+1)
=(x2+1)(x3+8)
We find the zeroes of P by setting each factor equal to 0
Let x2+1=0
x=1
x=±i
Let x3+8=0
x3=8
x=2
Therefore, the zeroes of P are ±i,2

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