The Proot Function; The Quot And Remainder Functions; The Peval Function; Fractions - HP 50g User Manual

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,
2
from X +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 (X) and P (X). In other words, they provide the values of Q(X) and R(X)
1 2
from P (X)/P (X) = Q(X) + R(X)/P
1 2
Thus, we can write: (X
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)'.

The PEVAL function

The function PEVAL (Polynomial EVALuation) can be used to evaluate a
polynomial
p(x) = a
given an array of coefficients [a
The result is the evaluation p(x
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))'
Page 5-9
2
QUOT('X^3-2*X+2', 'X-1') = 'X^2+X-1'
REMAINDER('X^3-2*X+2', 'X-1') = 1.
3
-2X+2)/(X-1) = X
n n-1
x +a x
n n-1
, a
n
). Function PEVAL is not available in the
0
(X). For example,
2
+X-1 + 1/(X-1).
2
+ ...+ a x +a
2
, ... a , a , a
n-1 2 1
x+ a ,
1 0
] and a value of x
0
.
0