SOLUTION: For the polynomial P(x)=2x^3+5x^2-3x-4
A. Use Descartes' Rule to analyze the zeros of the function.
B. Use the Rational Zeros Theorem to identify the possible rational zeros.
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A. Use Descartes' Rule to analyze the zeros of the function.
B. Use the Rational Zeros Theorem to identify the possible rational zeros.
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Question 430001: For the polynomial P(x)=2x^3+5x^2-3x-4
A. Use Descartes' Rule to analyze the zeros of the function.
B. Use the Rational Zeros Theorem to identify the possible rational zeros.
I am really having a hard time figuring this out, I would appreciate any help on this!
Descartes Rule of Signs: Remembering that the lead coefficient, lacking a minus sign, is a positive coefficient, step from one term to the other counting the number of times the sign changes from + to - or - to +.
I count 1. Therefore there is exactly 1 positive root.
If you replace x with -x, you get
And then you count two sign changes. Hence there are exactly 2 or 0 negative roots.
The rational roots theorem says the possible rational roots are all rational numbers of the form
where is an integer divisor of the constant term and is an integer divisor of the lead coefficient.
So
are your possible rational roots.
John
My calculator said it, I believe it, that settles it
