Question

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

Answer 1

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(1)=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.