HP 50g manual Fractions, Proot function, Quot and Remainder functions, Peval function

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 X2+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, P1(X) and P2(X). In other words, they provide the values of Q(X) and R(X) from P1(X)/P2(X) = Q(X) + R(X)/P2(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: (X3-2X+2)/(X-1) = X2+X-1 + 1/(X-1).

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) = an⋅xn+an-1⋅x n-1+ …+ a2⋅x2+a1⋅x+ a0,

given an array of coefficients [an, an-1, … a2, a1, a0] and a value of x0. The result is the evaluation p(x0). 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))’

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