Question 106515: Hello,
I've never tried this before, but I'm having a lot of difficulty understanding and remembering all the steps in solving large polynomial equations. One in particular is as follows:
a)Use Descartes Chart to show all possible combinations of positive, negative, and imaginary zeros.
b)Use Rational Zero Theorem to show all possible rational zeros to the given polynomial equation.
c)Find an upper bound and lower bound for all zeros using the Bounds Theorem.
d)Using the above information and synthetic division to find all real and imaginary zeros of the polynomial.
Thank you so much in advance for all your help. This stuff is so intense, and I'd like some help finding ways to remember everything that goes into this and when to apply it. Thanks again!
Andrew
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! f(x) = 36x^9-72x^8-61x^7+104x^6+2x^5+58x^4+71x^3-94x^2-28x+24=0
f(-x) = -36x^9-72x^8+61x^7+104x^6-2x^5+58x^4-71x^3-94x^2+28x+24=0
a)Use Descartes Chart to show all possible combinations of positive, negative, and imaginary zeros.
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f(x) has 4 changes of sign :there are 4, or 2, or 0 positive rational zeros.
f(-x) has 5 changes of sign: there are 5, or 3, or 1 negative rational zeros.
The coefficients are Real: there are 0, or 2, or 4,or 6, or 8 imaginaries.
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b)Use Rational Zero Theorem to show all possible rational zeros to the given polynomial equation.
They have the form p/q where p is an divisor of 24 and q is a divisor of 36.
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c)Find an upper bound and lower bound for all zeros using the Bounds Theorem.
Not familiar with the "Bounds Theorem".
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d)Using the above information and synthetic division to find all real and imaginary zeros of the polynomial.
x=(-2/3) , x=(1/2) , x=(2/3), x=(3/2), x=2
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Comment: I got these zeroes by graphing and using the CALC/zero function
on a TI-83. It looks like there are 4 imaginary zeros which you could
find using synthetic division with the zeros I have listed above.
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Cheers,
Stan H.
Thank you so much in advance for all your help. This stuff is so intense, and I'd like some help finding ways to remember everything that goes into this and when to apply it. Thanks again!
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