use the rational zero theorem to find all the real zeros of polynomial, use the zeros to factor f over the real numbers f(x)=11x^3-x^2+11x-1 x= f(x) =show work
The rational zero theorem says that if the zeros of the polynomial `f(x)` are rational, then numerators are positive or negative factors of the constant term -1, and the denominators are positive factors of the leading coefficient 11.
This means we can look at any of the possible roots:
`+-1` , `+-1/11`
Starting with `x=1/11` , we see that
`f(1)=1/121-1/121+1-1=0` so `x-11` is a factor.
With factoring, we see then that
So the only real root is `x=1/11` .