By the rational root theorem, we can see that one(1) is root.
Now, create a synthetic division chart.
-1 |_1__1___-3____1_
This leaves us with the polynomial: x^2 + 2x - 1=0
Here, we can use the quadratic formula to get: x1=−1+√2,x2=−1−√2.
Thus, the roots of the equation p(x)=x^3+x^2-3x+1 are x1=1,x2=−1+√2,x3=−1−√2,