MHB Find x- and y- Intercepts....4

[mathdad]

Find the x- and y-intercepts.

y = 2x^5 - 5x^4 + 5

Let x = 0

y = 2(0)^5 - 5(0)^4 + 5

y = 5

The y-intercept is y = 5 and it takes place at the point (0,5).

Let y = 0 to find the x-intercept.

0 = 2x^5 - 5x^4 + 5

I am stuck here.

 

[Greg]

I don't think $0 = 2x^5 - 5x^4 + 5$ has roots that can be expressed in terms of elementary functions.

 

[mathdad]

More "nice" roots, right?

 

[Greg]

There's always a solution(s) for polynomials of degree 4 and lower (if one includes complex-valued results). Once we reach a degree of 5 we are, in general, out of luck (so to speak) but there are some quintics (polynomials of degree 5) that are solvable. I don't think the one we have here is, though.

A useful online tool is W|A (Wolfram Alpha). I will suggest that you familiarize yourself with this tool as it can aid insight into problems that may be difficult. :D

 

[MarkFL]

For any polynomial of degree 3 or more that doesn't succumb to the rational roots theorem to get down to a combination of linear/quadratic factors, I rely on numeric root finding techniques to approximate the real roots (and those are the only roots we need for finding intercepts). :D

 

[mathdad]

You are saying that "nice" roots in this case require advanced techniques. I am not there yet. I get it now.