# What are the roots of #x^4-6x^3+14x^2-14x+5=0# with their multiplicities?

The roots are:

#x=1# with multiplicity#2#

#x=2+-i# each with multiplicity#1#

Given:

We can factor the remaining quadratic by completing the square and using the difference of squares identity:

So the remaining two zeros are:

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The roots of the equation (x^4 - 6x^3 + 14x^2 - 14x + 5 = 0) with their multiplicities are:

- ( x = 1 ) (Multiplicity 2)
- ( x = 1 + i ) (Multiplicity 1)
- ( x = 1 - i ) (Multiplicity 1)

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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