# What are all the possible rational zeros for f(x)=3x^3+5x^2-11x+3 and how do you find all zeros?

Aug 21, 2016

The zeros are: -3;-1/3 and $1$.

#### Explanation:

To find the rational zeros of a polynomial with integer coefficients we use the Rational Roots Theorem .

In this example we have:

p,q in {-3;-1;1;3} so

p/q in {-3;-1/3;-1;1/3;1;3}

We can easily guess that $f \left(1\right) = 0$, so $1$ is our first zero.

To find other roots we can either check the remaining values (the theorem says there are no other rational zeros) or divide the polynomial by $x - 1$ and find the roots of resulting quadratic expression.