Question about Casio FX-115ES Scientific Calculator

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Find root of polynomial equation (has imaginary parts) on FX-115ES

Will this calculator find the roots of an equation such as:

X-9th + 30X-8th + 401X-7th + 3176X-6th + 16696X-5th + 61400X-4th + 160324X-3rd + 287344X-sqrd + 318448X + 163340

If so, how is it done?

Thanks,

Scott

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  • Anonymous Apr 18, 2008

    I need help with a similar polynomial equation. (I'm going to fail!)

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6 Suggested Answers

  • 1 Answer

SOURCE: My Ti-89 won't factor a quadratic equation with imaginary roots.

(a-b)3

Posted on Apr 04, 2009


  • 7987 Answers

SOURCE: how to factor a polynomial equation on casio fx-300es?

Hello,
The Casio FX-300ES does not handle symbolic algebra. So it cannot factor a general polynomial expression. The methods can be found in any book on Algebra.
However if you are interested in approximate factorization of quadratic and cubic polynomials, you can use the calculator to do that. It can solve aX^3 +bX^2+cX+d =0 and the quadratic equations.

If you want to factor a cubic polynomial P3(X) = aX^3+bX^2+cX+d , you write the corresponding cubic equation as aX^3+bX^2+cX=d =0 , then you divide all terms of the equation by a to obtain

X^3+(b/a)X^2+(c/a)X+(d/a)=0.

You use the calculator to solve (approximately) this equation.
Suppose you find the 3 roots X1,X2,and X3. Then the polynomial X^3+(b/a)X^2+(c/a)X+(d/a) can be cast in the factored form (X-X1)(X-X2)(X-X3) and the original polynomial P3(X) can be written as

P3(X) = a*(X-X1)(X-X2)(X-X3)

You can handle the quadratic polynomial the same way.

P2(X) =a*(X-X1)(X-X2) where X1, X2 are the two real roots

Hope it helps.

Posted on Oct 17, 2009

  • 7987 Answers

SOURCE: How do I solve a polynomial equation:

Hello,

Sorry, but what you wrote is not an equation but a polynomial expression. You want to solve the equation x^4+5x^3-3x^2-43x-60 =0.

The solve( command, can only be used with real numbers.
The solve( is available through the CATALOG : [2nd][CATALOG], scroll down till you reach the command. Highlight it and press [ENTER]. The command echodes on main screen as solve( .
You complete the command by entering the expression (not the equation), the name of the variable you solve for, the initial guess , and { lower limit, upper limit} between curly brackets, and the closing parenthesis.
Exemple:
solve (x^4+5x^3-3x^2-43x-60 , x,0 {-5,0} ) [ENTER]
should give you the negative root,
solve (x^4+5x^3-3x^2-43x-60 , x,0 {0,5} ) [ENTER]
should give you the positive root.

It is implied that the expression is 0, so you should not insert =0, otherwise you get an error. Here for the lower limit is -5 you must use the change sign symbol (-) under the 3 key, not the regular MINUS.

You may ask how I knew that there were two roots when the equation is a quartic? By first graphing it to have an idea about where the roots lie and how many there are. You should always do that to speed up the search.

There is another way to zoom in on the roots: by drawing the graph and using the tools accessible under the [2nd][CALC] menu, namely the option [2:Zero]
The resolution of the TI83/84 is not good enough for this function that grows too fast, but I am inserting a picture of the curve from another calculator with a much better resolution.

56ccf66.jpg

Hope it helps.


Posted on Oct 18, 2009

  • 7987 Answers

SOURCE: trying to graph polynomial equation and

Hello,
Before starting to graph Y= function, you should Turn STATPLOTS off.
Press [2nd][STATPLOTS] [4:PlotsOff]. command echoes ob screen as PlotsOff . Press [ENTER] to execute it. Calc answers Done.
Press [MODE]
See if Func, (4th line) is already highlighted.
If it is press Y= to start entering the functions.
If it is not highlighted, scroll down to 4th line, then use arrow to highlight Func an press ENTER.

Then press Y= and enter the function. You see that as you enter the function the equal sign becomes highlighted white on dark. Finish entering the sunction and press ENTER. Cursor move to Y=2. Make sure that the equal sign for Y1= is still highlighted. If not, move the cursor on it and press [ENTER].

You can enter the variable X by pressing the [X,T,theta,,n] button to the right of the green [ALPHA] key. Or, alternatively, you press [ALPHA] [STO->] (X).

To graph Press [GRAPH]. If you do not see anything on screen, it may be due to the window dimensions. You can modify the window by pressing the [WINDOW] button.

To test you configuration, I suggest you graph Y1=e^(x) and Y2= ln(x)
e9fbf22.jpg

You access the exponential e by [2ND] [LN] (e^x) and the natural log by pressing [LN]. In each case you have to enter the right parenthesis.
This what you should get.
d4c87a8.jpg
If you are not familiar with these function, just enter Y1=X and you will see a staright line passing through the origin (0, 0), just like the one on the following screen capture.


2aeab91.jpg
Hope it helps.

Posted on Oct 20, 2009

  • 96627 Answers

SOURCE: how to get the imaginary

You need to be in complex mode before you can do any calculations involving complex numbers. Press MODE 2 to switch to CMPLX mode. When you're done, press MODE 1 to switch back to COMP mode. (Yes, the names are confusing. I didn't pick them.)

Posted on Dec 14, 2010

  • 96627 Answers

SOURCE: I can't plug in "i" on my casio fx-115ES even when

By default the calculator only works with real numbers. To use complex numbers, press MODE 2 to switch to complex mode.

Posted on Mar 05, 2011

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1 Answer

I want to solve an complex equation on casio fx-570 ES Plus


Your scientific calculator is unable to solve complex equation with complex coefficients. You should try to solve by hand directly using the quadratic formula or by factoring the polynomial in z
failing that, another way would be to set z=x+iy, substitute this for z, carry out the algebra and try to separate real and imaginary parts. But your two equations will constitute a system of two quadratic equations. I am not aware of any general method to solve coupled nonlinear equations.
Good luck.

Dec 20, 2012 | Casio FX-115ES Scientific Calculator

1 Answer

Edit Casio FX - 9860G SD have complex equations??


Thhe Casio FX-9860G SD can solve a polynomial equation of degree 2 or 3 with REAL coefficients. If the complex MODE is set to REAL it will find the real roots. If the complex mode is set to a+ib, it will find the real and complex roots.

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

Addendum.
The calculator CANNOT solve equations with complex coefficient. YOU can however convert the system of linear equations with ccomplex coefficients ( of the type you show) as a system of 4 linear equations in 4 unknowns; Split x into a real and an imaginary part, split y into a real and an imaginary part. Substitute Real(x)+iIm(x) for variable x in the equations; substitute Real(y)+iIm(y) for y in the two equations; do the algebra. In each of the original equations split the Real and imaginary parts. You should be able to derive 4 linear equations in unknowns Real(x), Im(x), Real(y), and Im(y).
Use the linear equation solver to obtain the solutions. Recompose x=Real(x)+iIm(x), and y=Real(y)+iIm(y)

Alternatively, after you create the system of 4 linear equations you can use the matrix utility to find Real(x), Im(x), Real(y) and Im(y) and recompose the x and y.

Mar 17, 2012 | Casio FX-9860G Graphic Calculator

1 Answer

Casio FX - 9860G SD have complex equations?? edit


The Casio FX-9860G SD can solve a polynomial equation of degree 2 or 3 with REAL coefficients. If the complex MODE is set to REAL it will find the real roots. If the complex mode is set to a+ib, it will find the real and complex roots.

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

Addendum.
The calculator CANNOT solve equations with complex coefficient. YOU can however convert the system of linear equations with ccomplex coefficients ( of the type you show) as a system of 4 linear equations in 4 unknowns; Split x into a real and an imaginary part, split y into a real and an imaginary part. Substitute Real(x)+iIm(x) for variable x in the equations; substitute Real(y)+iIm(y) for y in the two equations; do the algebra. In each of the original equations split the Real and imaginary parts. You should be able to derive 4 linear equations in unknowns Real(x), Im(x), Real(y), and Im(y).
Use the linear equation solver to obtain the solutions. Recompose x=Real(x)+iIm(x), and y=Real(y)+iIm(y)

Mar 17, 2012 | Casio Calculators

2 Answers

Can casio fx-991es factor?


No it cannot factor. It does not do symbolic manipulations.If you know a bit of theory of polynomials you can find the roots of the polynomial equation. The calculator has a Solve utility. Once you have the roots, you can use your knowledge about polynomials to carry out the factorization procedure.

Aug 31, 2011 | Casio fx-300ES Calculator

1 Answer

Is my fx-300 capable of factoring trinomials?


Sorry, but no! it is not capable of factoring anything. It can however solve for the roots of a polynomial equation.Write your polynomial as P(X)= a(X² +(b/a)X+c/a) =0. Use the calculator to solve the polynomial equation X² +(b/a)X+c/a =0 and find the roots X1, and X2. You will then be able to write the original polynomial as P(X)=a(X-X1)(X-X2). Beware that by using the calculator, the values of the roots are approximate.

Mar 14, 2011 | Casio fx-300ES Calculator

1 Answer

How to find roots of a polynomial using fx 115 ms


It depends on the degree of the polynomial.
If polynomial is od degree 2 or 3 you can use the EQN mode (the equation MODE) by pressing [MODE][5:EQN] to enter Equation mode then press [3] for quadratic polynomial or [4] for a cubic one.
You will then be prompted for the various coefficients. The canonical form of these polynomials is aX^2 plus bX plus c= 0, and aX^3 plus bX^2 plus cX plus d=0.

If polynomial is of degree higher than 3, or for a general non-linear equation you must use the Solve( feature. See example #017 on page 6 of the appendix to the manual.

Nov 28, 2010 | Casio FX-115ES Scientific Calculator

1 Answer

Can I factor a polynomial with a Casio fx-9750GII calculator


The short story is that this calculator does have a computer algebra system or CAS and thus cannot factor polynomials with arbitrary (unknown) coefficients or known coefficients.
However if the coefficients are given you can ,if you are willing to travel that way, factor approximately a polynomial P(x).
Basically, the idea is that any polynomial P(X) of degree n can be written in the factored form (X-x_1)(X-x_2)...(X-x_n), where x_1, x_2, x_3,...x_n are the roots (real or complex) of the equation P(X)=0.


The procedure ( for a 3rd degree polynomial) is as follows: (the fixYa site parser will remove the plus signs, so I am writing the whole word plus instead of the mathematical sign
If you want to factor a cubic polynomial P3(X) = aX^3 plus bX^2 plus cX plus d , you write the corresponding cubic equation as aX^3 plus bX^2 plus cX plus d =0 , then you divide all terms of the equation by a to obtain

X^3 plus (b/a)X^2 plus (c/a)X plus (d/a)=0.

You use the calculator to solve (approximately) this equation.
Suppose you find the 3 roots X1,X2,and X3. Then the polynomial X^3 plus (b/a)X^2 plus (c/a)X plus (d/a) can be cast in the factored form (X-X1)(X-X2)(X-X3) and the original polynomial P3(X) can be written as

P3(X) = a*(X-X1)(X-X2)(X-X3)

You can handle the quadratic polynomial the same way.
P2(X) =a*(X-X1)(X-X2) where X1, X2 are the two real roots.

To find the various roots you must use the solve( application.

Nov 11, 2010 | Casio FX-9750GPlus Calculator

1 Answer

How to factor a polynomial equation on casio fx-300es?


Hello,
The Casio FX-300ES does not handle symbolic algebra. So it cannot factor a general polynomial expression. The methods can be found in any book on Algebra.
However if you are interested in approximate factorization of quadratic and cubic polynomials, you can use the calculator to do that. It can solve aX^3 +bX^2+cX+d =0 and the quadratic equations.

If you want to factor a cubic polynomial P3(X) = aX^3+bX^2+cX+d , you write the corresponding cubic equation as aX^3+bX^2+cX=d =0 , then you divide all terms of the equation by a to obtain

X^3+(b/a)X^2+(c/a)X+(d/a)=0.

You use the calculator to solve (approximately) this equation.
Suppose you find the 3 roots X1,X2,and X3. Then the polynomial X^3+(b/a)X^2+(c/a)X+(d/a) can be cast in the factored form (X-X1)(X-X2)(X-X3) and the original polynomial P3(X) can be written as

P3(X) = a*(X-X1)(X-X2)(X-X3)

You can handle the quadratic polynomial the same way.

P2(X) =a*(X-X1)(X-X2) where X1, X2 are the two real roots

Hope it helps.

Sep 27, 2009 | Casio fx-300ES Calculator

1 Answer

How do you Factor a Polynomial on a Casio fx-300ES


Hello,
Sorry, but you cannot use this calculator to factorize a general polynomial.
1. It does not know symbolic algebra.
2. It can only manipulate numbers.

However if you have polynomials of degree 2 or 3, with numerical coefficients (no letters) you can set [MODE] to equation and use the equation solver to find the real roots of 2nd degree or 3rd degree polynomials. Assuming that your polynomials have real roots (X1, X2) for the polynomial of degree 2, or (X1, X2, X3) for the polynomial of degree 3, then it is possible to write
P2(X) =a*(X-X1)(X-X2)
P3(X)= a(X-X1)(X-X2)(X-X3)
This is an approximate factorization, except if your calculator configured in MathIO, has been able to find exact roots (fractions and radicals)
where a is the coefficient of the highest degree monomial aX^2 +...
or aX^3 +....

But I have a hunch that this is not what you wanted to hear.

Good luck.

Mar 08, 2009 | Casio fx-300ES Calculator

1 Answer

How to factor with this model


Hello,
Sorry, but you cannot use this calculator to factor a general polynomial.
1. It does not know symbolic algebra.
2. It can only manipulate numbers.

However if you have polynomials of degree 2 or 3, with numerical coefficients (no letters) you can set [MODE] to Equation and use the equation solver to find the real roots of 2nd degree or 3rd degree polynomials. Assuming that your polynomials have real roots (X1, X2) for the polynomial of degree 2, or (X1, X2, X3) for the polynomial of degree 3, then it is possible to write

P2(X) =a*(X-X1)(X-X2)
P3(X)= a(X-X1)(X-X2)(X-X3)


where a is the coefficient of the highest degree monomial aX^2 +...
or aX^3 +....

This is an approximate factorization, except if your calculator configured in MathIO, has been able to find exact roots (fractions and radicals)

While the [MODE][5:Equation] only handles quadratic and cubic equations, the [SHIFT][SOLVE=] solver finds the roots of arbitarry expressions (not limited to polynomials). In principle you can use it to find the roots of an expression. If it is a polynomial of dgree higher that 3 you can factor it (approximately).

But I have a hunch that this is not what you wanted to hear.

Hope it helps.

Dec 09, 2008 | Casio fx-300ES Calculator

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