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Question

The number of distinct real roots of the cubic polynomial equation x3−3x2+3x−1=0 is

A
1
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B
3
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C
0
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D
2
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Solution

The correct option is A 1
Given: f(x)=x33x2+3x1=0

Let's substitute x=1 in f(x), we get:
f(1)=133(1)2+3(1)1=0

Hence, we know that
x=1 is a root of f(x) or (x1) is its factor.
Apply divison algorithm,
f(x)=(x1)(x22x+1)
f(x)=(x1)(x2+(11)x+(1)(1))
f(x)=(x1)(x1)(x1)
Roots of f(x)=0 are x=1,1,1
So number of distinct real roots is 1.

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