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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
n
x
n
+ a
n-1
x
n-1
+ …+ a
1
x +
a
0
= 0. The fundamental theorem of algebra indicates that there are n solutions
to any polynomial equation of order n. Some of the solutions could be complex
numbers, nevertheless. As an example, solve the equation: 3s
4
+ 2s
3
- s + 1 =
0.
We want to place the coefficients of the equation in a vector [a
n
,a
n-1
,a
1
a
0
].
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@@ Select solve poly...
„Ô3‚í2‚í 0
‚í 1\‚í1@@OK@@ Enter vector of coefficients
@SOLVE@ Solve equation
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: