Question
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Tutor-Verified Answer
Answer
x = 2
Solution
To find the roots of the factored polynomial
, we need to set the expression equal to zero and solve for
.
Since any number raised to the power of 3 that equals zero must be zero itself, we can solve for
by setting the base equal to zero:
Now, add 2 to both sides to solve for
:
The root of the polynomial is
. Since it’s a cubic polynomial and the exponent is 3, the root
is a root of multiplicity 3. This means that
is the only root of the polynomial, and it occurs three times.
So, the roots of the polynomial are:
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Mind Expander
To find the roots of the polynomial
, we set the polynomial equal to zero:
To solve for
, we take the cube root of both sides:
Solving for
, we have:
Since the factor
appears three times, the root
has a multiplicity of 3. Therefore, the complete list of roots is:
So, the final answer is:
x = 2, 2, 2