Trident Help

Natural Scientific 991 manual · Chapter 15 of 18

Equations

Solve two to four simultaneous linear equations, or a polynomial of degree 2 to 4.

15.1Solve simultaneous equations#

Press MENU, press (−) (the key with the red A legend) to open Equation/Func, choose 1 (Simul Equation) and the number of unknowns (2, 3 or 4). Fill the coefficient form row by row: for 2x + y = 5 type 2, 1 and 5 (a1, b1, c1). Press = after each box. Solutions are exact fractions when possible.

Example 15.1

2x + y = 5 and x − y = 1

  1. Open Equation, Simul, 2 unknowns.

    MENU(−)12

  2. First equation: 2, 1, 5.

    2=1=5=

  3. Second equation: 1, -1, 1.

    1=(−)1=1=
Result of the example "2x + y = 5 and x − y = 1" The display shows: x=2 / y=1.
You should seex=2 y=1
Example 15.2

A fractional solution

  1. x + y = 1 and x − y = 0.

    MENU(−)121=1=1=1=(−)1=0=
Result of the example "A fractional solution" The display shows: x=1/2 / y=1/2.
You should seex=1/2 y=1/2
Example 15.3

Three unknowns

  1. x+y+z=6, 2x−y+z=3, x+2y−z=2.

    MENU(−)131=1=1=6=2=(−)1=1=3=1=2=(−)1=2=
Result of the example "Three unknowns" The display shows: x=1 / y=2 / z=3.
You should seex=1 y=2 z=3
Example 15.4

No solution

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

    MENU(−)121=1=1=1=1=2=
Result of the example "No solution" The display shows: No Solution / [AC] :Cancel / [◀][▶]:Goto.
You should seeNo Solution
Example 15.5

Infinitely many solutions

  1. x + y = 2 and 2x + 2y = 4.

    MENU(−)121=1=2=2=2=4=
Result of the example "Infinitely many solutions" The display shows: Infinite Solution / [AC] :Cancel / [◀][▶]:Goto.
You should seeInfinite Solution
Choosing the number of unknowns The display shows: Number of Unknowns? / 2:2 Unknowns / 3:3 Unknowns / 4:4 Unknowns.
Choosing the number of unknowns

15.2Solve a quadratic equation#

Choose 2 (Polynomial) and then the degree. For degree 2 type a, b and c of ax² + bx + c = 0, pressing = after each. Roots are shown exactly, including square roots and complex values, followed by the x and y of the vertex with a Minimum or Maximum label.

Example 15.6

x² − 5x + 6 = 0

x2−5x+6=0x^2-5x+6=0

  1. Equation, Polynomial, degree 2.

    MENU(−)22

  2. a = 1, b = -5, c = 6.

    1=(−)5=6=
Result of the example "x² − 5x + 6 = 0" The display shows: x1=3 / x2=2 / x-Value Minimum=5/2 / y-Value Minimum=-1/4.
You should seex1=3 x2=2 x-Value Minimum=5/2
Example 15.7

Roots with square roots

  1. x² − 5x + 3 = 0.

    MENU(−)221=(−)5=3=
Result of the example "Roots with square roots" The display shows: x1=(5+√13)/2 / x2=(5-√13)/2 / x-Value Minimum=5/2 / y-Value Minimum=-13/4.
You should seex1=(5+√13)/2 x2=(5-√13)/2
Example 15.8

Complex roots

  1. x² + 2x + 5 = 0.

    MENU(−)221=2=5=
Result of the example "Complex roots" The display shows: x1=-1+2i / x2=-1-2i / x-Value Minimum=-1 / y-Value Minimum=4.
You should seex1=-1+2i x2=-1-2i
Example 15.9

A double root

  1. x² − 2x + 1 = 0.

    MENU(−)221=(−)2=1=
Result of the example "A double root" The display shows: x=1 / x-Value Minimum=1 / y-Value Minimum=0.
You should seex=1
x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
The quadratic formula used for degree 2

15.3Solve a cubic or quartic equation#

For degree 3 type a, b, c and d; for degree 4 type a to e. All roots are listed, real or complex, calculated numerically.

Example 15.10

x³ − 6x² + 11x − 6 = 0

  1. Polynomial, degree 3.

    MENU(−)23

  2. 1, -6, 11, -6.

    1=(−)6=11=(−)6=
Result of the example "x³ − 6x² + 11x − 6 = 0" The display shows: x1=3 / x2=2 / x3=1.
You should seex1=3 x2=2 x3=1
Example 15.11

x⁴ − 5x² + 4 = 0

  1. Polynomial, degree 4.

    MENU(−)241=0=(−)5=0=4=
Result of the example "x⁴ − 5x² + 4 = 0" The display shows: x1=2 / x2=1 / x3=-1 / x4=-2.
You should seex1=2 x2=1 x3=-1 x4=-2

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