# How do you find all the zeros of # f(x)= x^4+x^3+2x^2+4x-8# with its multiplicities?

##### 1 Answer

First, we use the rational root theorem to try and pick out a possible root. I always try 1 first because it is easy to do: just count the sum of the coefficients. Luckily enough, it worked!

So now we synthetically divide

x1 1 1 2 4 -8

1 2 4 8

result1 2 4 8 0

so now we have

Applying guess and check work for the rational root theorem again, we find that

So we go back to synthetic division

x-2 1 2 4 8

-2 0 -8

Result 1 0 4 0

Now we have

We use the quadratic formula to find that the other two roots are

So finally, our zeroes are