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

f(x) = x4 x3 − 19x2 − 11x + 31

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Graph of f(x) = x4 x3 − 19x2 − 11x + 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) = x4 − x3 − 19x2 − 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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