Question 947522
the rational roots are all the possible factors of p divided by q after you have reduced that fraction to simplest terms.


p is the constant term.
q is the leading coefficient.


your p is equal to 5
your q is equal to 3


the possible factors of 5 are 1,5
the possible factors of q are 1,3


the possible factors of p/q are 1/1, 1/3, 5/1, 5/3.


the possible rational roots are plus or minus the possible factors of p/q.


as it turns out, the roots are x = -1 and x = 5/3.


a graph of the equation is shown below:


<img src = "http://theo.x10hosting.com/2015/021401.jpg" alt="$$$" </>


1.667 shown on the graph is equal to 1 and 2/3 which is equal to 5/3.


the solution of x = -1 is actually encountered twice, so the factors of the equation are:


(x+1) * (x+1) * (x-5/3) = 0


if you multiply those factors out, you will get back to the original equation.


so you have 3 rational roots to the equation.


-1 is encountered twice and 5/3 is encountered once.