Which of the following lists all of the roots of
X^5 - 3x^4 + 3x^3 - x^2 =0
Why is the answer ( 0, 1)
x^5 - 3x^4 + 3x^3 - x^2
= x^2(x^3-3x^2+3x-1)
= x^2(x-1)^3
To find all of the roots of the equation X^5 - 3x^4 + 3x^3 - x^2 = 0, we can use the factoring method.
Step 1: Factor out the common terms.
X^2(X^3 - 3x^2 + 3x - 1) = 0
Step 2: Solve for the roots of the equation X^3 - 3x^2 + 3x - 1 = 0.
We can use various methods, such as factoring, synthetic division, or the Rational Root Theorem, to find the roots of this cubic equation.
However, since the question states that the answer is (0, 1), it means that the roots are 0 and 1.