Figure A-10.2(a), a graph of the cubic polynomial , suggests that the equation has three real roots. The graph is drawn with the Plot Builder, launched from the Context Panel for the polynomial.
The Context Panel for the polynomial will contain the Solve option, and Maple will assume that the polynomial is set equal to zero.
Choosing the Solve≻Solve option results in the three exact solutions shown (compressed) in Table A-10.2(a).
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plot(x^3-9*x^2-2*x+15,x=-2..10,y=-110..40,color=red);
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Figure A-10.2(a) Graph of left-hand side of given equation.
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, where
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Table A-10.2(a) Compressed form of the exact roots of
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Each (expanded) solution contains "I," Maple's notation for , making it seem that the roots are complex. But a cubic with real coefficients must have at least one real root. And Figure A-10.2(a) suggests the roots are all real. They are, but converting them to the form , where b = 0, requires steps such as those sketched in Table A-10.2(b) where the first root in Table A-10.2(a) is transformed by applying the indicated Context Panel options.
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, where
and
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Approximate≻10 (digits)
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Table A-10.2(b) Schematic for transforming the first root to the form , where b = 0.
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The more reasonable alternative to working with such complicated exact expressions for the roots of equations would be finding numeric solutions with the Solve option "Solve Numerically." This results immediately in the three floating-point roots .
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Control-drag the polynomial.
Press the Enter key.
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Context Panel: Solve≻Numerically Solve
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