Question

x^3-4x+1=0 Solve Using Rational Root Theorem

Answer 1

\[x^3-4x+1=0\]

Answer 2

you need to find integers such that a|coefficient of leading x and b|constant term, then a/b will give possible rationnal roots, but you still have to check them. Keep in mind that if m|n,n|m then m=+-n
so a=+-1
b=+-1
thus possible roots are +-1.Lets check
-1+4+1=4
1-4+1=-2
We see that neither satisfies the polynomial
thus it does not have rationnal roots
NOTE: it does not mean the polynomial does not have roots at all, just no rationnal ones