Question
Find the roots of the factored polynomial.
Ask by Sanders Cummings. in the United States
Dec 19,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The roots are 0 and 1.
Solution
The roots of the polynomial
are the values of
that make the polynomial equal to zero.
Set the polynomial equal to zero:
This equation is satisfied when:
-
⟹ -
⟹
So, the roots are:
0, 1
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Extra Insights
To find the roots of the factored polynomial
, we can set the equation equal to zero:
This gives us two factors to consider:
For the first factor
, the root is:
For the second factor
, the root is:
However, since
contributes a double root at
, we can list the roots as:
You can write the distinct roots as
or include their multiplicities as
. For the sake of simplicity, the final answer as a list of distinct values is: