|
•
|
The graph of in Figure A-10.4(a) suggests the equation has just one real root, and therefore three pairs of complex-conjugate roots.
|
|
•
|
In general, a seventh-degree polynomial will not have solutions expressible as radicals, and even if it did, the expressions would most likely be very cumbersome.
|
|
•
|
Hence, the expectation here is a numeric solution via the Solve≻Numerically Solve (w/complex) option in the Context Panel.
|
|
|
>
|
plot(P,x=-1.5..1,y=-3..2);
|
|
|
Figure A-10.4(a) Graph of
|
|
|
|
|
|
|
•
|
Control-drag the polynomial and press the Enter key.
|
|
•
|
Context Panel: Solve≻Numerically Solve (w/complex)
|
|
|
|
|
|
It certainly would be nice if Maple would display the roots as per Table A-10.4(a).
|
|
|
|
|
|
|
|
|
Table A-10.4(a) Roots of the equation
|
|
|
The solution given by the Solve≻Numerically Solve (w/complex) option in the Context Panel is the simplest interactive solution. The alternatives below are far more tedious to implement and are not really recommended in this context.
|
•
|
The Context Panel option Solve≻Numerically Solve provides just the real solution, .
|
|
•
|
The Context Panel option Solve≻Obtain Solutions for≻x returns all seven solutions as a sequence of RootOf structures, of the form
|
where k ranges from 1 to 7. Each member of this sequence has to be extracted to a separate line (easiest by Control-drag or copy/paste) so that the Approximate option in the Context Panel can be applied. The results for , are the complex conjugate pairs listed in Table A-10.4(a).
