Question

Can you help me solve this: x^4-5x^2+2x+11=0

Answer 1

Try using the Rational Root Theorem and Descartes' Rule of Signs.

Answer 2

and what is that sorry! :)

Answer 3

Rational Root Theorem:
If we have a polynomial of the form:
\[
P(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_0
\]Then, the only possible rational roots are those of the form, where \(p\) is any factor of \(a_0\) and \(q\) is a factor of \(a_n\):
\[
x=\pm\frac{p}{q}
\]So, in your case, our possible roots:
\[
x=\{\pm\frac{1}{1}, \pm\frac{11}{1}\}
\]Descartes' Rule of Signs is better by the net: http://www.purplemath.com/modules/drofsign.htm

Answer 4

wow all this look very confusing can you help me solve my problem please =D @LolWolf

Answer 5

All right, so, using synthetic division/plugging in numbers, we try every root possible. If \(x=1\):
\[
(1)^4-5(1)^2+2(1)+11=0
\]Etc. And find that there are no real roots to the equation. And, we are done.

Answer 6

really! we're done

Answer 7

I mean to say that there are no *rational* solutions to the equation, just for future reference.

Answer 8

ah okay i see