real and complex zeros
- Thread starter jjde
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mmm4444bot
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?
(Ummm, equations do not have zeros; equations have solutions, functions have zeros, and polynomials have roots.)
I would start by using the Rational Roots Theorem, to find a root of the polynomial.
(Use your text's index, to look it up.)
Once you find a root, you know a factor, yes?
Once you know a factor, you can divide to get another factor, yes?
Once you know all of the factors, you can find all of the solutions to the given equation.
If you've learned how to divide polynomials synthetically, the whole process goes relatively quickly; otherwise, you'll need to divide longhand (which is not hard).
If you find yourself stuck trying to apply the Rational Roots Theorem, or you do not understand something I wrote, please ask specific questions, show us what you tried, or explain what you're thinking.
(Ummm, equations do not have zeros; equations have solutions, functions have zeros, and polynomials have roots.)
I would start by using the Rational Roots Theorem, to find a root of the polynomial.
(Use your text's index, to look it up.)
Once you find a root, you know a factor, yes?
Once you know a factor, you can divide to get another factor, yes?
Once you know all of the factors, you can find all of the solutions to the given equation.
If you've learned how to divide polynomials synthetically, the whole process goes relatively quickly; otherwise, you'll need to divide longhand (which is not hard).
If you find yourself stuck trying to apply the Rational Roots Theorem, or you do not understand something I wrote, please ask specific questions, show us what you tried, or explain what you're thinking.
Try
http://oakroadsystems.com/math/polysol.htm
I think this site document is a little long, but it has an example of syntetic division. In this example explains how to find the possible real roots.
In your particular case, the possible roots are: 1/2, 1, 2, 4, 8 16 (all of them positive and negative, 12 possibilities in total)
The actual roots of your polynomial are: 2,2,-1,-4
I hope this helps,
garf
http://oakroadsystems.com/math/polysol.htm
I think this site document is a little long, but it has an example of syntetic division. In this example explains how to find the possible real roots.
In your particular case, the possible roots are: 1/2, 1, 2, 4, 8 16 (all of them positive and negative, 12 possibilities in total)
The actual roots of your polynomial are: 2,2,-1,-4
I hope this helps,
garf