Trident Help

Natural Color Graphing manual · Chapter 16 of 18

Equations

Simultaneous equations with 2 to 6 unknowns, polynomials of degree 2 to 6, and a general solver.

16.1Open the Equation app#

Press MENU then 5. The bar offers SIMUL (F1), POLY (F2) and SOLVER (F3).

The Equation app The display shows: Equation / F1:Simultaneous / F2:Polynomial / F3:Solver / SIMUL POLY SOLVER · · ·.
The Equation app

16.2Solve simultaneous equations#

Press F1 (SIMUL) and then the number of unknowns (F1 for 2, F2 for 3, and so on up to 6). Fill in the grid row by row: for 2x + 3y = 8 type 2, 3 and 8. Press EXE after each value and F1 (SOLVE) at the end. F2 (DELETE) clears a value and F3 (CLEAR) clears the whole grid.

Example 16.1

2x + 3y = 8 and x − y = −1

  1. SIMUL, 2 unknowns, then the rows 2, 3, 8 and 1, -1, -1.

    MENU5F1F12EXE3EXE8EXE1EXE(−)1EXE(−)1EXEF1
Result of the example "2x + 3y = 8 and x − y = −1" The display shows: Simul 2 / X=1 / Y=2.
You should seeX=1 Y=2
Example 16.2

Three unknowns

  1. Three equations with a solution (5, 3, -2).

    MENU5F1F21EXE1EXE1EXE6EXE0EXE2EXE5EXE(−)4EXE2EXE5EXE(−)1EXE27EXEF1
Result of the example "Three unknowns" The display shows: Simul 3 / X=5 / Y=3 / Z=-2.
You should seeX=5 Y=3 Z=-2
Example 16.3

Fractional solutions

  1. x + y = 1 and x − y = 0.

    MENU5F1F11EXE1EXE1EXE1EXE(−)1EXE0EXEF1
Result of the example "Fractional solutions" The display shows: Simul 2 / X=1/2 / Y=1/2.
You should seeX=1/2 Y=1/2
Example 16.4

No solution

  1. x + y = 1 and x + y = 2.

    MENU5F1F11EXE1EXE1EXE1EXE1EXE2EXEF1
Result of the example "No solution" The display shows: No Solution / Press:[EXIT].
You should seeNo Solution
Example 16.5

Infinite solutions

  1. x + y = 1 and 2x + 2y = 2.

    MENU5F1F11EXE1EXE1EXE2EXE2EXE2EXEF1
Result of the example "Infinite solutions" The display shows: Infinite Solution / Press:[EXIT].
You should seeInfinite Solution

16.3Solve a polynomial equation#

Press F2 (POLY) and pick the degree (F1 is degree 2 up to F5 for degree 6). Type the coefficients from the highest power, pressing EXE after each, then F1 (SOLVE). Real and complex roots are listed, exact when they can be.

x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
The quadratic formula
Example 16.6

x² − 3x + 2 = 0

  1. POLY, degree 2, 1, -3, 2, SOLVE.

    MENU5F2F11EXE(−)3EXE2EXEF1
Result of the example "x² − 3x + 2 = 0" The display shows: Poly 2 / x1=2 / x2=1.
You should seex1=2 x2=1
Example 16.7

Roots with square roots

  1. x² − 2 = 0.

    MENU5F2F11EXE0EXE(−)2EXEF1
Result of the example "Roots with square roots" The display shows: Poly 2 / x1=√2 / x2=-√2.
You should seex1=√2 x2=-√2
Example 16.8

Complex roots

  1. x² + 2x + 5 = 0.

    MENU5F2F11EXE2EXE5EXEF1
Result of the example "Complex roots" The display shows: Poly 2 / x1=-1+2i / x2=-1-2i.
You should seex1=-1+2i x2=-1-2i
Example 16.9

A cubic

  1. x³ − 6x² + 11x − 6 = 0, degree 3.

    MENU5F2F21EXE(−)6EXE11EXE(−)6EXEF1
Result of the example "A cubic" The display shows: Poly 3 / x1=1 / x2=2 / x3=3.
You should seex1=1 x2=2 x3=3
Example 16.10

A quartic

  1. x⁴ − 1 = 0, degree 4.

    MENU5F2F31EXE0EXE0EXE0EXE(−)1EXEF1
Result of the example "A quartic" The display shows: Poly 4 / x1=-1 / x2=1 / x3=-i / x4=i.
You should seex1=-1 x2=1 x3=-i x4=i

16.4Solve any equation (SOLVER)#

Press F3 (SOLVER). Type an equation using ALPHA=. for the equals sign and press EXE; the calculator asks for a starting value for each variable. Press F6 (SOLVE) to get X, plus Lft and Rgt, the two sides at the solution.

Example 16.11

Solve x² = 2

  1. Type X² = 2, EXE, starting value 1, SOLVE.

    MENU5F3X,θ,Tx²ALPHA=.2EXE1EXEF6
Result of the example "Solve x² = 2" The display shows: Solver / X=1.414213562 / Lft=2 / Rgt=2.
You should seeX=1.414213562 Lft=2 Rgt=2

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