Find all zeros of the polynomial. P(x)=x^{3}-2x^{2}+2x-1

Karen Simpson

Karen Simpson

Answered question

2021-12-10

Find all zeros of the polynomial.
P(x)=x32x2+2x1

Answer & Explanation

Joseph Fair

Joseph Fair

Beginner2021-12-11Added 34 answers

Step 1
Given:
P(x)=x32x2+2x1
Step 2
To find the zeroes of the polynomial P(x), we need to solve the equation P(x)=0.
P(x)=0
x32x2+2x1=0
x3x2x2+x+x1=0
x2(x1)x(x1)+1(x1)=0
(x1)(x2x+1)=0
x1=0,x2x+1=0
x=1,x2x+1=0
We shall solve, x2x+1=0
x=(1)±(1)24×1×12×1
x=1±32
x=1±3i2
x=12±32i
Therefore, the zeroes of the given polynomial are, 1,12+32i,1232i

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