Use the Rational Zeros Theorem to find the possible zeros of the following polynomial function: #f(x)=2x^3-9^2+10x-3#?

1 Answer
Feb 27, 2016

First, I always like to start off the rational root theorem by using x = 1.
This is because it is very easy to quickly count a possibility: just count the coefficients.

So we do #2 - 9 + 10 - 3#

And from there we were able to quickly find a root, #x = 1 #

Now, we just synthetically divide

x1 2 -9 10 -3
2 -7 3
Result 2 -7 3 0

So now, after dividing by #x-1#, we have #2x^2 - 7x + 3#

If you see the factors, you can just factor it. Otherwise, use the quadratic formula

#(7 +- sqrt(49 - 24))/4#

#(7 +-5)/4#

So we have either 3 or 1/2.

Do not forget the #x=1# that we already found, and we have zeroes at 1/2, 1, and 3