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.
Algebra.Com
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!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
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
\ =\ -2x^3\ +\ 5x^2\ +\ 3x\ -\ 4)
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
RELATED QUESTIONS
use descartes rule of signs to determine the possible number of positive real zeros and... (answered by Edwin McCravy)
find a rational zero of the polynomial function and use it to find all the zeros of the... (answered by stanbon)
Use Descartes' Rule of Signs to determine the possible number of positive and negative... (answered by stanbon,jim_thompson5910)
use descartes rule of signs to determine the possible number of positive and negative... (answered by Fombitz)
Use Descartes rule of signs to determine how many positive and how many negative real... (answered by mukhopadhyay)
Use Descartes' Rule of Signs to state the number of possible positive and negative real... (answered by stanbon)
For the function f(x) = 3x^4- 4x^3 +x^2+ 6x-2
a. State the degree of the polynomial.... (answered by josgarithmetic)
4.6
The following function is given.
f(x)=x^3 -5x^2 -9x+45
a. List all rational... (answered by Boreal)
With the polynomial: f(x) = 5x^3 + 8x^2 -4x + 3
a. The Fundamental Theorem of Algebra (answered by solver91311)
