Question about The Learning Company Achieve! Math & Science Grades 1-3 (381933) for PC, Mac

Real zeros of polynomial equation

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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.

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

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)

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 Office Equipment & Supplies

You can do it two ways.

**Graphically:**

Open the graph utility, enter a function y1= expression(x) where expression(x) is the polynomial. Graph the function y1(x). Play with the window dimensions to display the interesting part of the graph. You can then see if there are any zeros (roots).

While the graph is displayed, press SHIFT F5 (G-Solv). Press F1:Root to look for a root. Read the value of the root at the bottom of the screen (to the left).

**Solve utility**

Open the QEquation solver, select F2:polynomial, or F3: solver.

The polynomial solve can solve polynomial equations up to degree 6.

The solve solve polynomial and any other type of non algebraic equations

Open the graph utility, enter a function y1= expression(x) where expression(x) is the polynomial. Graph the function y1(x). Play with the window dimensions to display the interesting part of the graph. You can then see if there are any zeros (roots).

While the graph is displayed, press SHIFT F5 (G-Solv). Press F1:Root to look for a root. Read the value of the root at the bottom of the screen (to the left).

Open the QEquation solver, select F2:polynomial, or F3: solver.

The polynomial solve can solve polynomial equations up to degree 6.

The solve solve polynomial and any other type of non algebraic equations

Mar 16, 2012 | Casio CFX 9850GA Plus Calculator

One way is to use the Polynomial Root Finder and Simultaneous Equation Solver app.

Press the APPS key, then select PlySmlt2 and press ENTER. Press ENTER to get past the opening screen, then select "POLY ROOT FINDER" and press ENTER. Select the order of the polynomial and other settings as desired. Press F5 (the GRAPH key) to go to the next screen. Enter the polynomial coefficients, then press F5 to solve. The next screen will show you the roots (unless you selected real roots and the polynomial doesn't have any real roots).

If you don't have the app installed, you can download it from

http://education.ti.com/educationportal/sites/US/productDetail/us_poly_83_84.html

Press the APPS key, then select PlySmlt2 and press ENTER. Press ENTER to get past the opening screen, then select "POLY ROOT FINDER" and press ENTER. Select the order of the polynomial and other settings as desired. Press F5 (the GRAPH key) to go to the next screen. Enter the polynomial coefficients, then press F5 to solve. The next screen will show you the roots (unless you selected real roots and the polynomial doesn't have any real roots).

If you don't have the app installed, you can download it from

http://education.ti.com/educationportal/sites/US/productDetail/us_poly_83_84.html

Jan 20, 2011 | Texas Instruments TI-83 Plus Calculator

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.

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

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.

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

You use the calculator to solve (approximately) this equation.

Suppose you find the 3 roots

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

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:

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.

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:

If you want to factor a cubic polynomial P3(X) = aX^3 bX^2 cX d , you write the corresponding cubic equation as

You use the calculator to solve (approximately) this equation.

Suppose you find the 3 roots

You can handle the quadratic polynomial the same way.

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

Sep 11, 2010 | Casio FX-9750GPlus Calculator

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.

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

You use the calculator to solve (approximately) this equation.

Suppose you find the 3 roots

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

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.

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

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.

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

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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