Question

Can someone explain to me how to find the zeros of a polynomials function? I need to find it for this: 2x^3-9x+3

Answer 1

You can try looking for them using Rational Root Theorem and synthetic division.

Answer 2

what is that?

Answer 3

If you have a polynomial of third degree or higher, and it can't be factored, you're essentially stuck with a guess-and-check process.

Answer 4

The RRT lets you know which rational roots (if any) it could have, so you know what to guess at first.
Take all the factors of the constant at the end and divide each of them by all the factors of the leading coefficient to get all the possible combinations of rational numbers which might be roots of the polynomial.

Answer 5

In your example, the constant is 3, and the leading coefficient is 2, so the factors of 3 are {1, 3} and the factors of 2 are {1, 2}, so all the possible rational roots are ±{1, 1/2, 3, 3/2}.

Answer 6

Do you know how to do synthetic division?

Answer 7

probably but I don´t know what it is by name

Answer 8

It would look like this for this polynomial:

Answer 9

The zero is there as a placeholder for the missing x^2 term.

Answer 10

ok

Answer 11

is that it?

Answer 12

That's the method to start with to try to find a rational zero, if it exists. After you find one of the zeroes, you can factor it out of that cubic polynomial and be left with a quadratic polynomial and then find the other 2 zeroes using the quadratic equation.

Answer 13

Graphing points as you go is also a good idea because that can help show you where to look next for a possible zero.

Answer 14

this sounds really complicated, is there an easier way?

Answer 15

Sometimes you get lucky and the polynomial is factorable, but this one doesn't look like it will yield that easily.
It seems a little complicated at first because there are a handful of theorems to understand to know how it works, but it's a straight-forward enough method to just plug away at until it works.

Answer 16

Having some experience with synthetic division makes it a lot easier and actually rather quick depending on how lucky your guesses are. I can give some other tips that will help make your guesses luckier, but it basically boils down to finding at least one rational root and then you might be able to use some other method to find the other zeroes.

Answer 17

Can you take it from here, or do you need more explanation? I can show a couple more steps to help get you started.