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Answer:
The 6th degree polynomial is
Step-by-step explanation:
Zeros of a function:
Given a polynomial f(x), this polynomial has roots such that it can be written as:
, in which a is the leading coefficient.
Zero 1 with multiplicity 3.
So
Zero 4 with multiplicity 2.
Considering also the zero 1 with multiplicity 3.
Zero -3 with multiplicity 1:
Considering the previous zeros:
Degree is the multiplication of the multiplicities of the zeros. So
3*2*1 = 6
The 6th degree polynomial is
We can check the equation is an extraneous solution or not by finding the solution and plugging it in the equation, to verify it.
<h3>What is the extraneous solution?</h3>In mathematics, an extraneous solution is a solution that comes from the process of solving the problem but is not a genuine solution to the problem, such as the answer to an equation.
As we know from the definition the extraneous solution is a solution that comes from the process of solving the problem but is not a genuine solution to the problem.
Let's suppose the equation is:
Squaring both the sides:
x + 4 = (x - 2)²
x + 4 = x² - 4x + 4
x² -5x = 0
x = 0 or x = 5
Checking for the solution by plugging in the equation;
3 = 3
2 ≠ -2
The solution x = 0 shows extraneous solution.
Thus, we can check the equation is an extraneous solution or not by finding the solution and plugging it in the equation, to verify it.
Learn more about the extraneous solution here:
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