Texas Instruments TI-89 Titanium User Manual page 871

zeros()
MATH/Algebra menu
expression
zeros( ,
Returns a list of candidate real values of
make
expression
exp8list(solve(
For some purposes, the result form for
more convenient than that of
result form of
solutions, solutions that require inequalities, or
solutions that do not involve
Note: See also
expression1
zeros({
varOrGuess2 [
Returns candidate real zeros of the simultaneous
algebraic
specifies an unknown whose value you seek.
Optionally, you can specify an initial guess for a
variable. Each
variable
– or –
=
variable
For example,
If all of the expressions are polynomials and if you
do NOT specify any initial guesses,
the lexical Gröbner/Buchberger elimination method
to attempt to determine all real zeros.
For example, suppose you have a circle of radius r
at the origin and another circle of radius r centered
where the first circle crosses the positive x-axis.
Use
zeros()
As illustrated by r in the example to the right,
simultaneous polynomial expressions can have
extra variables that have no values, but represent
given numeric values that could be substituted later.
Each row of the resulting matrix represents an
alternate zero, with the components ordered the
same as the
the matrix by [
868
) ⇒
var list
=0. does this by computing
zeros()
=0, .
expression var ,var
) )
. However, the
solve()
cannot express implicit
zeros()
.
var
, , and
cSolve() cZeros()
expression2 varOrGuess1
, }, {
}) ⇒
... ] matrix
,
, where each
expressions varOrGuess
must have the form:
varOrGuess
-
real or non real number
is valid and so is .
x x=3
zeros()
to find the intersections.
list. To extract a row, index
varOrGuess
].
row
zeros(aù x^2+bù x+c,x) ¸
that
var
{
ë( bñ-4øaøc-+b)
2øa
aù x^2+bù x+c|x=ans(1)[2] ¸
is
exact(zeros(aù (
zeros()
(sign (x)ì 1),x)) ¸
exact(solve(aù (
(sign (x)ì 1)=0,x)) ¸
.
solve()
,
uses
zeros({x^2+y^2ì r^2,
(xì r)^2+y^2ì r^2},{x,y}) ¸
Extract row 2:
ans(1)[2] ¸
Appendix A: Functions and Instructions
}
bñ-4øaøc-b
2øa
e
^(x)+x)
e ^(x)+x)
x
e
+ x = 0 or x>0 or a = 0

r
3

2 2

ë
r

2

ë
r

2
0
{}

ør


ør
3

2

ør
3

2