**Solution 1: Graphically.** The roots are given by the *x*-intercepts.

*f*(*x*) = *x*^{4} −* x*^{3} − 19*x*^{2} − 11*x* + 31

Graph of *f*(*x*) = *x*^{4} −* x*^{3} − 19*x*^{2} − 11*x* + 31

We see that there are 4 roots, at approximately

x= -3,x= -2,x= 1,x= 5.

**Solution 2:** Using "Compute → Solve → Numeric" in Scientific Notebook:

f(x) =x^{4}− x^{3}− 19x^{2}− 11x+ 31,Solution is: {

x= -2.97}, {x= -2.05}, {x= 1.02}, {x= 4.99}.

We see that the roots are close to our estimation from the graph.

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