Find all the real zeros of the polynomial

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: \(x_1=-1+\sqrt{2}, x_2=-1-\sqrt{2}\).

 

Thus, the roots of the equation p(x)=x^3+x^2-3x+1 are \(x_1=1, x_2=-1+\sqrt{2}, x_3=-1-\sqrt{2}\),