HP 49g Graphing Calculator - Manual (Page 135)

Solving polynomial equations
PolpioiTiial equations are of the form;
a.r" + bx” % ,.. + cx^ + dx + e = 0
For example, the following equation is a third order polynoixiial:
5x'" + 4a:“ - 3x + 2 = 0
You can use the HP 49G to:
® find the roots of a polynomial
® find the coefficients of a polynomial, given a set of roots.
To solve a polynomial, you express it as a vector of its coefficients. For
example, consider the previous example:
5/ + 4;r^__3,x + 2 = 0
In vector fonn, this can be expressed as follows:
[5 4 ~3 2]
Note that if a polynomial does not include a term for a particular power,
you need to include a 0 in the vector to represent the term. For example:
Equation
3x + 5
Vector
3 0
Sv'"* - 2x
[5 0 -2 0]
Example
This example describes how to find the roots of the polynomial equation
5x^ + 4x^ - 3x + 2 = 0.
1. Open the numeric solver and select
solve
POLY
to display the Coefficients input form.
SOLVE
Cocfficimti [ 3:
Ent«zr Cfgffici^ht5 or SOLVE
Solving equations Page 6-5