Find all possible rational zeros for the following polynomial :
P(x) = 3x^3 -2x^2 -5x-2
Give an explanation to how as well.

Question

Find all possible rational zeros for the following polynomial :
P(x) = 3x^3 -2x^2 -5x-2
Give an explanation to how as well.

shamil98 · Answer

@wio

anonymous · Answer

This should help: http://en.wikipedia.org/wiki/Rational_root_theorem

campbell_st · Answer

do you know if the curve actually has a rational root..?

anonymous · Answer

Basically you have to guess and check:$$
\pm \frac{1,2}{1,3}
$$

shamil98 · Answer

So you substitute ? for p(1), p(2)..

anonymous · Answer

So for example: $$
\frac 11, -\frac 11, \frac 21, -\frac 21, \frac 13, -\frac 13, \frac 23, -\frac 23
$$These are all potential solutions.

anonymous · Answer

So you can check each one and hope they're a root.

shamil98 · Answer

That seems like a tedious job.. plugging in all those numbers especially with the equation being so long lol

anonymous · Answer

Well you know there are only 3 roots.

campbell_st · Answer

doing a quick mental arithmetic check there is a root between 1 and 2, which isn't rational

anonymous · Answer

If you find one of the roots, you can divide out $x-r$ where $r$ is the root. Then you have a quadratic equation.

shamil98 · Answer

What does the term "rational zeros" implicate? ..

campbell_st · Answer

and doing a quick check to the left of zero... looking for change in signs, there doesn't appear to be any other roots...

campbell_st · Answer

rational means the value can be written as a fraction 

e.g. 0.33333... = 1/3

a rational number is any number that can be written as a/b where a and b are integers

shamil98 · Answer

Okay.

shamil98 · Answer

So, rational zeros are any value that is rational? lol

campbell_st · Answer

a rational zero is a value which  cuts or touches the horizontal axis and is a rational number...

shamil98 · Answer

thank you guys for the explanation. I'm a bit more knowledgeable of math now. :)