Polynomial Equations - HP 50g User Manual

Polynomial Equations

Using the Solve poly... option in the calculator's SOLVE environment you can:
(1) find the solutions to a polynomial equation;
(2) obtain the coefficients of the polynomial having a number of given roots;
(3) obtain an algebraic expression for the polynomial as a function of X.
Finding the solutions to a polynomial equation
A polynomial equation is an equation of the form: a
a = 0. The fundamental theorem of algebra indicates that there are n solutions
0
to any polynomial equation of order n. Some of the solutions could be complex
numbers, nevertheless. As an example, solve the equation: 3s
0.
We want to place the coefficients of the equation in a vector [a
For this example, let's use the vector [3,2,0,-1,1]. To solve for this polynomial
equation using the calculator, try the following:
‚Ϙ˜@@OK@@
„Ô3‚í2‚í 0
‚í 1\‚í1@@OK@@
@SOLVE@
The screen will show the solution as follows:
Press ` to return to stack. The stack will show the following results in ALG
mode (the same result would be shown in RPN mode):
To see all the solutions, press the down-arrow key (˜) to trigger the line
editor:
n
x + a
n n-1
Select solve poly...
Enter vector of coefficients
Solve equation
n-1
x + ...+ a x +
1
4 3
+ 2s - s + 1 =
,a ,a a ].
n n-1 1 0
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