Question

Find all the possible rational zeros of the following polynomial: f(x) = 3x^3 − 20x^2 + 33x − 9

Answer 1

define descartes rule of sign for me

Answer 2

@amistre64 basically it is the change from number to number if 5x -5x that is one change

Answer 3

smartscores are out, looks lke another no notif day on openstudy ....

Answer 4

but yes, we count the number of changes in 'sign'.

postive roots are when we have a postivie x, negative with a negative x

so i just use x=1 and x=-1 to represent them.

notice that (-1)^odd = -1 so that effectively just reverses the sign on odd powers

Answer 5

Yes but what changes when you want to find rational zeros?

Answer 6

ah misread it ... rational zeros come from a pool of options that are constrcuted from the 'leading' coefficient and the constant tem

Answer 7

if it has a rational zero, then it must be of the form:\[\pm\frac{first.coeff.factors}{last.term.factors}\]

Answer 8

soh we have to find the factors for 3x^3 and 9?

Answer 9

well, 3 and 9 yes

Answer 10

well 3 and 1 for 3 and 3 and 3 for 9?

Answer 11

\[\pm\frac{1,3}{1,3,9}\]
what are all the possible combinations for this? this creates a pool of options for the only possible ratioanl roots that it can have

Answer 12

well 1*9 and 3*3 is that what you mean?

Answer 13

1/1, 1/3, 1/9
3/1, 3/3, 3/9

simplify and a set has no duplicate elements

1/1 = 3/3 so 1 is a solution

Answer 14

possible solution

Answer 15

1/3 = 3/9 so 1/3 is the possible solution

Answer 16

3/1 which is 3 is 3 a possible solution?

Answer 17

yes, it has no duplication so there is no other element to compare it to is all

Answer 18

1/1, 1/3, 1/9
3/1, 3/3, 3/9


1, 1/3, 1/9
3, 1, 1/3


1, 1/3, 1/9, 3 +- of course

Answer 19

Thank you for the helpa

Answer 20

yep