HP 50G - The PROOT Function; The QUOT and REMAINDER Functions; The PEVAL Function; Fractions

Page 5-9
The PROOT function
Given an array containing the coefficients of a polynomial, in decreasing
order, the function PROOT provides the roots of the polynomial. Example,
from X
2
+5X+6 =0, PROOT([1, –5, 6]) = [2. 3.].
The QUOT and REMAINDER functions
The functions QUOT and REMAINDER provide, respectively, the quotient
Q(X) and the remainder R(X), resulting from dividing two polynomials,
P
1
(X) and P
2
(X). In other words, they provide the values of Q(X) and R(X)
from P
1
(X)/P
2
(X) = Q(X) + R(X)/P
2
(X). For example,
QUOT(‘X^3-2*X+2’, ‘X-1’) = ‘X^2+X-1’
REMAINDER(‘X^3-2*X+2’, ‘X-1’) = 1.
Thus, we can write: (X
3
-2X+2)/(X-1) = X
2
+X-1 + 1/(X-1).
The PEVAL function
The function PEVAL (Polynomial EVALuation) can be used to evaluate a
polynomial
p(x) = a
n
⋅x
n
+a
n-1
⋅x
n-1
+ …+ a
2
⋅x
2
+a
1
⋅x+ a
0
,
given an array of coefficients [a
n
, a
n-1
, … a
2
, a
1
, a
0
] and a value of x
0
.
The result is the evaluation p(x
0
). Function PEVAL is not available in the
ARITHMETIC menu, instead use the CALC/DERIV&INTEG Menu. Example:
PEVAL([1,5,6,1],5) = 281.
Additional applications of polynomial functions are presented in Chapter 5
in the calculator’s user’s guide.
Fractions
Fractions can be expanded and factored by using functions EXPAND and
FACTOR, from the ALG menu (
‚×). For example:
EXPAND(‘(1+X)^3/((X-1)*(X+3))’)=‘(X^3+3*X^2+3*X+1)/(X^2+2*X-3)’
EXPAND(‘(X^2)*(X+Y)/(2*X-X^2)^2)’)=‘(X+Y)/(X^2-4*X+4)’
FACTOR(‘(3*X^3-2*X^2)/(X^2-5*X+6)’)=‘X^2*(3*X-2)/((X-2)*(X-3))’
NOTE: you could get the latter result by using PARTFRAC:
PARTFRAC(‘(X^3-2*X+2)/(X-1)’) = ‘X^2+X-1 + 1/(X-1)’.
SG49A.book Page 9 Friday, September 16, 2005 1:31 PM