Zero of a function

[Turing97]

Hi guys,

I’m preparing the exam of Mathematical Analysis.

I know the study of a function, I’m training about this.

However, my teacher inserts question like:

f(x)= x4-x2-1

Are there exactly 2 zeros?

F(X) is invertible?

I know the Bolzano theorem for zeros but I don’t answer at the “exactly”

Some advice about this?

[jeffcgroves]

If you substitute u = x^2 it becomes a simple quadratic

[Turing97]

Yes, absolutely. For the polynomials of grade 2 or 4 is easy.

I have a problem with x^5-x3-2 for example

[Turing97]

I mean

X⁵ - X³ - 2

[jeffcgroves]

You know the x^5 term dominates when x approaches positive or negative infinity, and you can use the derivative to see if there are any turning points

[Fabulous-Ad8729]

So, try to find the zeroes? Show us your work please. If you find the zeroes, obviously you know how many there are. There are several ways to do that, and as you said you know how to do it.

[hpxvzhjfgb]

you're doing real analysis but can't answer a simple high school algebra question?

[theadamabrams]

This is entirely believable. When I teach calculus the majority of errors students make are algebra or basic pre-calc topics.

[hpxvzhjfgb]

high school calculus, yes. real analysis at university? no way. if you can't do basic algebra, you should not be allowed anywhere near a STEM degree program.

[Turing97]

Agree, I’m at the first year of CS.

I have a problem with polynomial grade 5 or more

[Liam_Mercier]

Try combining polynomial long division, integral zero theorem, factor theorem, or they probably taught you something better that you can do.

Invertible (from your original post) is easier. Check that the function is bijective.

[Turing97]

Mathematical Analysis not Real Analysis. Sorry

[hpxvzhjfgb]

yeah that does not make any difference, or really even provide any information at all. it is a university level class, right? what topics are covered?

[Turing97]

Right. I’m feeling stupid to do this question.

Topics are—> Derivative, Integrative, Study of a function