How do you find all zeros of f(x)=x3+2x2−5x−6?

1 Answer
Alan P.
Jun 1, 2015

With no immediately obvious solutions, one way to attempt this is to plot the graph of the function.
Note that this does not guarantee that the x-intercepts will be exactly as they seem but it gives us some values to consider.
graph{x^3+2x^2-5x-6 [-10, 10, -5, 5]}
The graph of f(x)=x3+2x−5x−6
suggests that the solution set might be xε{−3,−1,+2}

We can check this by using these values for a factoring:
XXXXX(x+3)(x+1)(x−2)

Multiplying these possible factors we find that, in fact,
XXXXX(x+3)(x+1)(x−2)=x3+2x2−5x−6
so
the values previously considered to be merely "possible" have been verified as correct.

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