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

1 Answer
Aug 21, 2016

Answer:

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.