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The calculator cannot do symbolic algebra. If equation is aX^2+bX+c=0, write it in the form a(X^2+(b/a)X+(c/a))=0 and solve the quadratic equation X^2+(b/a)X+(c/a)=0. Get the approximate roots X1, and X2 (if they exist) and write your original equation in the for
Your quadratic polynomial is factored as a(X-X1)(X-X2)
Use the quadratic formula, or factor the quadratic polynomial. Once factored into a product of two first degree binomials, the roots are obtained by setting (in TURN) each binomial factor equal to zero.
The polynomial cannot be factored in the set of Real numbers: The roots of the polynomial equation are complex.
You should use the command cFactor( found under F2:Algebra> A:Complex>2:cFactor(
However, you should set the Mode Complex>Rectangular, and the EXACT/APPROXIMATE mode to Exact, otherwise your roots will be in decimal representation.
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.
Press MODE 5 to bring up the equation types. Press 3 for the quadratic. Enter the three coefficients. Press = to see the first root. If the display shows x1 then press down to see the other other root. If the display only shows x then that's a double root. Given the two roots x1 and x2, the factors of the quadratic are (x-x1) and (x-x2).
Refer to "Equation Calculations" on page E-55 of the manual and examples #094 and #095 in the appendix for examples of solving quadratic equations. If the you need the manual and/or appendix, you can download them from http://support.casio.com/manualfile.php?rgn=1&cid=004001004
you checked the calculator's manual to see if the calculator is able
(natively) to handle functions of a complex argument. It is able to
handle simple algebra with complex numbers, powers, roots, solving a polynomial equation. For this calculator, the hyperbolic functions must have a real argument otherwise you get a
error. But just to make sure, try the exponential function with i
(imaginary unit) as argument. If it comes back with a domain error you
have your answer.
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
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