Question

can anyone please help me or explain to me how to use the rational zero theorem???

Answer 1

ok... for rational zero theorem

find the factors of the constant call them p

find the factors of the coefficient of the leading term, call them q

then a rational zero will be p/q

as a simple example

P(x) = 2x^2 +3x + 1

the factors of the constant are -1, 1

the factors of the coefficient of the leading term are -1, -2, 1, 2

so a rational zero exists at p/q so look at the possibles

-1/1 and 1/-1 are the same so -1

1/-2, 1, 1/2

now test using

P(-1), P(-1/2), P(1), P(1/2)

and in doing so you see P(-1) = 0
P(-1/2) = 0

then rational zeros exist at x = -1 and x = -1/2

checking the polynomial can be factored.

(2x + 1)(x + 1) = 0

x = -1/2, -1

thats a simple question but shows the process.

Answer 2

how do you get :"the factors of the constant are -1, 1 the factors of the coefficient of the leading term are -1, -2, 1, 2" ?? @campbell_st

Answer 3

this might help:
http://www.sparknotes.com/math/algebra2/polynomials/section4.rhtml

Answer 4

what numbers multiply to 1 -1 x -1 = 1 and 1 x 1 = 1

Answer 5

would you mind helping me out with this question @campbell_st ??
f(x)=2x^(4)+5x^(3)-8x^(2)-4x-7

Answer 6

ok... so the factors of 7

\[\pm 1, \pm 7\]

factor of 2\[\pm 1, \pm 2\]

so you need to look at

P(1/2), P(7/2) P( -1/2) P(-7/2) P(7/1), P(-7/1), P(1/1) P(-1/1)

I'd start with

P(1) and P(-1)

see if either are equal to zero.

Answer 7

@jmprz_793
please check this out:
http://openstudy.com/users/some_someone#/updates/5158c14ee4b07077e0c0a6aa

it is a question previously asked by another user about the rational zero theorem.

@campbell_st and I were explaining step by step.

Answer 8

I just pick up my calculator and solve it...

Answer 9

and you may want to check you have entered the equation correctly... as I only get 2 solutions. x = -3.54714 and x = 1.60699