Question

Find all rational roots for P(x)=0
P(x)=3x^3+x^2-8x-12

Answer 1

??

Answer 2

Try the Brio-Ruffini Method.

Answer 3

what is that?

Answer 4

Is the same of Synthetic method.

Answer 5

Can you demonstrate?

Answer 6

Wait

Answer 7

well try the rational root theorem

find the factors or -12 call them p

and the factors of 3 call them q

then the rational roots will be p/q

so

\[p = \pm 1, \pm 2, \pm3, \pm4, \pm6, \pm12\]

and

\[q = \pm1, \pm 3\]

Answer 8

I'd start with 2, -2, 3, and -3

so if

P(2) = 0 x = 2 is a rational root

Answer 9

Woah you lost me

Answer 10

What is p=/pm etc

Answer 11

ok, the rational root theorem is used to get an idea of what numbers could be the roots of a polynomial...

so you have

you find the possible by finding the factors of the constant term... -12

and the factors of the coefficient of the leading term 3

Answer 12

omg im so sorry my internet connection is so bad it translated your comment into something completely irrelevant.

Answer 13

well for example

-1 *-3 = 3 so -1 and -3 can be factors of 3

as well as 1 * 3 = 3

but as a guess I'd try f(2)

Answer 14

No, yes, I understand, continue. So sorry

Answer 15

ok... so you are looking at

1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12

as possible solutions...

as well as

1/3 -1/3 2/3, -2/3, 4/3, -4/3

when you get a rational root, you can do some synthetic division or polynomial division to find the quadratic factor

Answer 16

another method is to just graph the curve... find the points where it cuts the x-axis

Answer 17

Couldn't find a root for this one P(x)=2x^4-x^3-14x+7

Answer 18

lol... for this one, I'd graph it... there isn't anything obvious...

there is a root between 0 and 1

so try 1/2