So there are graphs on my page, and the textbook is asking
"Explain wether the graph might represent a polynomial function that has zeros of order 2 or of order 3."
What are they asking there?
"Explain wether the graph might represent a polynomial function that has zeros of order 2 or of order 3."
What are they asking there?
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In the factorization of a polynomial, a zero of order n would be represented n times. Here is an example:
p(x) = (x - 4)(x - 7)²(x + 1)³
The zeros are 4, 7, and -1. The 7 is of order 2 and the -1 is of order 3. If the order of a root is greater than one, then the graph of y = p(x) is tangent to the x-axis at that value.
Edit:
I should add that if the zero has an odd order, the graph crosses the x-axis at that value. If the zero has an even order, the graph touches the x-axis there, with a local minimum or a maximum.
p(x) = (x - 4)(x - 7)²(x + 1)³
The zeros are 4, 7, and -1. The 7 is of order 2 and the -1 is of order 3. If the order of a root is greater than one, then the graph of y = p(x) is tangent to the x-axis at that value.
Edit:
I should add that if the zero has an odd order, the graph crosses the x-axis at that value. If the zero has an even order, the graph touches the x-axis there, with a local minimum or a maximum.