Sketch a graph of a polynomial function that is degree 5 with all real zeros, a positive leading coefficient, one negative zero, and two positive zeros.
you can just tell me the polynomial cuz I'm not sure if you can post images here
(x+1) for negative 0
(x-1)(x-1)(x-2)(x-2) for 2 positive zeros (must repeat to get total of 5)
so
y = (x+1)(x-1)(x-1)(x-2)(x-2)
you multiply :)
Ok thank you so much!!
To sketch a graph of a polynomial function with the given criteria, we need to consider the characteristics of polynomial graphs.
First, let's determine the number of real zeros and their multiplicities. The polynomial function has a degree of 5, which means it can have a maximum of 5 real zeros. We are given that all of the zeros are real, so we know there are no complex zeros.
Next, we are given that there is one negative zero and two positive zeros. Since the multiplicities are not specified, we can assume all zeros have a multiplicity of 1.
Based on the leading coefficient being positive, we know that the graph begins in the bottom left quadrant and ends in the top right quadrant.
Given this information, we can make the following observations about the graph:
- The graph starts in the bottom left quadrant, approaches the x-axis, and crosses it at the negative zero.
- It then increases and crosses the x-axis at the two positive zeros, and possibly another one or two times.
- The graph also increases and goes towards the positive infinity on either side.
Since we do not have specific values for the zeros or the y-intercept, we can only roughly sketch the graph based on the information we have.
Here is a rough sketch of the graph:
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Please note that the exact shape and location of the graph depends on the specific values of the zeros and the leading coefficient, which we do not have. So, the sketch provided is a general representation of the graph based on the given criteria.