Finding a polynomial from a set of roots, Solving linear systems, Finding a polyiromial from a set of roots -7 – HP 49g Graphing Calculator User Manual
Page 137: Solving linear systems -7, Set of, Solve poly, Solve, Finding a polynomial from a, Roots
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Finding a polynomial From a
set of
roots
To find a polynomial equation that corresponds to a set of roots, use the
following procedure:
1. Open the numeric solver aird select
SOLVE POLY
to display the
Coefficients input form.
2.
Press ® to place the cursor in the Roots field, and press
edit
.
Matrix
Writer opens, ready for use.
•3. In Matrix Writer, enter the roots on the top row of the matrix, and
press (ENTE^ to place the values, in vector form, on the input form.
4. Press @ to place the cursor in the Coefficients field.
5. Press
SOLVE.
The nmneric solver solves the equation and places the
coefficients, in vector fonn, in the Coefficients field.
Solving linear systems
A linear system is a set of linear equations where there is more than one
independent variable. For example, the following is a system where there
are two linear equations and two independent variables.
3.r +2y = b
2 x ~ 8 y = 7
There are three types of linear systems:
• Exactly determined systems are systems where there is the same
number of equations as there are independent variables. The HP 49G
can solve these systems to the limits of its accuracy.
® Over-determined systems are systems where there is a greater
number of equations than there are independent variables. Usually
there is no exact solution to these systems. The HP 49G returns the
least-squares solution.
® Under-determined systems are systems where there is a smaller
number of equations than the number of independent variables.
Usually there is an infinite number of solutions to these systems. The
HP 49G returns the solution with the minimum Euclidean norm.
Solving equations
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