How do I simply something like this?

The question says: Graph and describe - (in the description i must include the roots, and their multiplicity) the easiest way I can think of finding the roots is to simplify this, however I've never simplified an function with the term x^{4 }so I'm not sure where to start.

f (x) =x^{4}-5x + 3

Re: How do I simply something like this?

I'm not sure what you mean by "simplify". That's about as simple as it is going to get. And, as for actually finding the roots, I doubt you will be able to do that. There is a "quartic equation" but it is very complicated.

You can, for example, use the "rational root theorem" that says that if is a root of a polynomial with integer coefficients then n must divide the leading coefficient and m must divide the constant term. Here the leading coefficient is 1 and the constant term is 3 which has only and as its divisors. It is easy to see that , , , and , none of which are 0 so all roots are irrational numbers.

You **can**, for example, determine that while, as above, the value at 1 is -1< 0. That means there must be a root between 0 and 1. so there is another root between 1 and 2. I believe, though I can't prove it, that the other two roots are not real numbers.

Re: How do I simply something like this?

Thanks for the response. Im in grade 12 applied math so I don't expect thats what they want me to do. I guess I'm supposed to use the graphing software provided for me to just identify the roots by seeing them, it just seemed a little too simple. Wow that was some confusing stuff there you just did.

Re: How do I simply something like this?

I expect you have a CAS calculator. Use its solve function to solve the equation .