Question

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

Answer 1

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