Hi! I was wondering if you guys could offer me help on the following problem. I am supposed to find the x-intercepts of this problem, but all of my attempts have failed. I have tried factoring it ,and I tried the Rational Zero Theorem. Thanks for your help!

Question

2x^4-7x^3+11x-4=0

Answer 1

This polynomial does not factor with rational coefficients, so you will need to use a numeric or graphical method. I'm not sure what tools you have at your disposal, but there are several good graphing calculators online, such as

http://www.wolframalpha.com/input/?i=2x%5E4-7x%5E3%2B11x-4

Answer 2

Thank you so much! I was debating whether or not I should use a graphing calculator for this problem. Is there a way I can determine if the graph touches or crosses at the x-axis without the calculator in this case?

Answer 3

Well, you can evaluate y at several places and you know that if it is positive at x1 and negative at x2, there is at least one root in between them. This can be repeated to the desired precision. You can use Descartes' Rule of Signs to figure how many positive or negative roots there might be. And you can use synthetic division sign checks to bound the range of the real roots.

Answer 4

Thanks!