Finding polynomial roots.
Find the roots of 25x2 + 12x + 1.69 = 0.
To find second-order polynomial roots, press 2nd [POLY].
Press 2.
Respond to the displayed prompts to enter the coefficients.
Press 25 ENTER
Press 12 ENTER
Press 1.69 ENTER
To view the results without reviewing the coefficients, press ALPHA N.
To view the next result, press ENTER .
Solving a real system of simultaneous equations.
The TI-68 can rapidly determine the solutions to a system of simultaneous equations
up to fifth order. This short demonstration solves a second-order system of
simultaneous equations for x and x2.
6x1 + 5x2 = 1
2x1 + 3x2 = 4
To begin solving a system of simultaneous equations, press 2nd [SIMUL].
To specify second order, press 2.
To specify a real system, press ALPHA N. Then enter the coefficients equation-by-equation.
Press 6 ENTER
Press 5 ENTER
Press 1 ENTER
Press 2 ENTER
Press 3 ENTER
Press 4 ENTER
To view the results without reviewing the coefficients, press ALPHA N.
To view the next result, press ENTER .
Solving a complex system of simultaneous equations.
Solve this second-order set of complex simultaneous equations to find x and x2.
Set the calculator to show answers to three places after the decimal so the entire result
can be seen without scrolling the display.
(6.8, 4.7)x1 + (9.3, 8.7)x2 = (1.1, 6.9)
(9.7, 2.3)x1 + (8.7, 5.5)x2 = (9.3, 8.8)
To set the fixed decimal, press 2nd [FIX] 3.
To begin solving a system of simultaneous equations, press 2nd [SIMUL].
To specify second order, press 2 .
To specify a complex system, press ALPHA Y. Then enter the coefficients equation-by-equation.
Press ( 6.8 , 4.7 ) ENTER
Press ( 9.3 8.7 ) ENTER
Press ( 1.1 , 6.9 ) ENTER
Press ( 9.7 , _ 2.3 ) ENTER
Press ( 8.7 , 5.5 ) ENTER
Press ( 9.3 , 8.8 ) ENTER
To view the results without reviewing the coefficients, press ALPHA N.
To view the next result, press ENTER.
To return the calculator to floating decimal operation, press 2nd [FIXI ___

Order 2-4?
A2=?
Al =?
AO=?
Review YN?
xl= (-0.24, 0.1)
x2= (-0.24, -0.1)
Equa 2-5?
Complex YN?
all = ?
a12 =?
b1 =?
a21 = ?
a22 =?
b2 = ?
Review YN?
x1 = -2.125
x2 = 2.75
Equa 2-5?
complex YN?
all =
a12 ?
a21 - ?
a22 -
b2 =
Review YN?
xl = (1.923, 1.187)
x2 = (-0.915, -0.242)
= (-0.915, -0.242)

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