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

zakinutuzi 2021-12-12 Answered
Find all zeros of the polynomial.
P(x)=x33x2+3x2
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Expert Answer

Mary Herrera
Answered 2021-12-13 Author has 37 answers
Step 1
Given polynomial is P(x)=x33x2+3x2
Step 2
To find zeros of the polynomial.
First find the rational zero of polynomial by using rational root test.
The rational root test is if the polynomial has a rational zero then it must be a fraction pq, where p is factor
of constant term and q is factor of leading coefficient.
Here p=-2 and q=1.
The factors of -2 are ±1,±2.
Now substitute possible values to find zeroes of polynomial.
For x=1, P(1)=(1)33(1)2+3(1)2=13=32=1
For x=2, P(2)=(2)33(2)2+3(1)2=812+4=0
Thus the one zero of the polynomial is x=2.
Step 3
Now divide the polynomial P(x)=x33x2+3x2 with x-2 get,
x33x2+3x2x2=x2x+1
x33x2+3x2=(x2)(x2x+1)
Now for x2x+1=0
x=(1)±(1)24(1)(1)2(1)
x=1±142
x=1±3i2
Therefore the zeroes of the polynomial P(x)=x33x2+3x2 are,
x=2,x=1+3i2,x=13i2

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Bukvald5z
Answered 2021-12-14 Author has 33 answers

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