HP 49g manual Variable, Pcoef function, Proot function, Quot and Remainder functions

The variable VX

Most polynomial examples above were written using variable X. This is because a variable called VX exists in the calculator’s {HOME CASDIR} directory that takes, by default, the value of ‘X’. This is the name of the preferred independent variable for algebraic and calculus applications. Avoid using the variable VX in your programs or equations, so as to not get it confused with the CAS’ VX. For additional information on the CAS variable see Appendix C in the calculator’s user’s guide.

The PCOEF function

Given an array containing the roots of a polynomial, the function PCOEF generates an array containing the coefficients of the corresponding polynomial. The coefficients correspond to decreasing order of the independent variable. For example:

PCOEF([-2, –1, 0 ,1, 1, 2]) = [1. –1. –5. 5. 4. –4. 0.],

which represents the polynomial X6-X5-5X4+5X3+4X2-4X.

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).

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