Question 489208: Using complete sentences, describe how you would find all possible rational zeros of the polynomial function f(x) = 4x3 – 5x2 + 9x – 6. Be sure to provide the answer in your explanation.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Using complete sentences, describe how you would find all possible rational zeros of the polynomial function f(x) = 4x3 – 5x2 + 9x – 6. Be sure to provide the answer in your explanation.
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f(x) = 4x3 – 5x2 + 9x – 6
Two ways you can work this problem.
The first way: if you are allowed to use a graphing calculator, find one of the rational zeros, if there is one, then calculate the remaining zeros by factoring or using the quadratic formula.
If you are not allowed to use a graphing calculator, you can use the rational roots theorem, which is a time-consuming process. I will be using the former process.
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The graphing calculator shows there is only one real but irrational root, 0.794454..., which means the other two roots are non-real or imaginary. I wonder what the purpose of this problem was as the answers are unusual. If you had chosen to use the rational roots method, it would have been most frustrating.
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