The POLY Menu

The POLY Menu is used to find all roots (or zeros) of any polynomial (up to 30th order).

Example 1: Find the roots of f(x) = x³ + 2x² - x - 2

The values needed to solve for the roots of a polynomial are its order and the coefficients of each of its terms. The initial screen prompts for the order:

POLY
order=3 (we type three and press enter since the order of the polynomial is 3)

The display now prompts us to enter the coefficients of our polynomial by displaying:

a3x^3+...+a1x+a0=0 (representing a₃x³ + a₂x² + a₁x + a₀ = 0) and then asking for each coefficient:
a3=1
a2=2
a1= -1
a0= -2

We type in the coefficents and press the down arrow or the enter key after each to move to the next one in the list. Missing terms in the polynomial they would have a coefficient of 0. Be sure to use the (-) key when entering negative coefficients. Now we press F5 to SOLVE for the roots. The display shows the 3 roots:

a3x^3+...+a1x+a0=0
x1= -2
x2= -1
x3=1

Enter its order and coefficients as before:
POLY
order=4

a4x^4+a3x^3+...+a1x+a0=0
a4=1
a3=2
a2=2
a1=2
a0=1

Now we press F5 to SOLVE for the roots. The display shows the 4 roots (2 are complex and 2 are equal):

a4x^4+a3x^3+...+a1x+a0=0
x1=(0, 1) representing the complex root x2 = i (after rounding 4.499...E-4 to 0)
x2=(0, -1) representing the complex root x3 = -i (after rounding 4.499...E-4 to 0)
x3=(-1, 0) (after rounding -1.00000031846 to -1)
x4=(-1, 0) (after rounding -.999999681543 to -1)