Items tagged with roots


hey guys ,


i have problem to obtain roots for a higher order equation


thanks for your

When I execute the following code in Maplesoft on my computer, there are no problems.  However when I execute the same code in mapleTA occasionally Maple only finds a single input value corresponding with h_given.  Anybody have any idea what is going on?

Basically I have a function, f,  that I am only interested in plotting and analyzing real-valued inputs, t, from =0 to 100 (or so).  At some point I assign an output value, h_given, and I wish to find the correlated real-valued inputs.  From the graph you can clearly see that there are 2 inputs, however the script occassionally only produces 1 output. (when running on mapleTA).

Thanks in advance,

a := MapleTA:-Builtin:-range(1800, 2300, 100):
b := (1/10)*MapleTA:-Builtin:-range(4, 8, 1):
timeT := MapleTA:-Builtin:-range(70, 100, 10):
f := -t*(b*t-b*timeT)^2*(cos(.15*t+4)^2-3)/a:
maxs := NLPSolve(f, t = 0 .. timeT, maximize):
maxim := maxs[1]:
graph := plot(f, t = 0 .. timeT, gridlines = true, 0 .. maxim+10, labels = [t, h(t)], labeldirections = [horizontal, vertical]);
h_given := 10;
expr := h_given-f:
answer_t := Student:-Calculus1:-Roots(expr, t = 0 .. timeT+5);
evalf(answer_t, 2);

I want to solve for the roots of a polynomial, such as a x^2+b x + c = 0, for which the output is only the positive root. All coefficients/variables in the polynomial are positive. 

Recently, someone posted an answer to a question where at some point they performed this task and their solution was really slick. But I can't find it. The answer used either solve, or eval or something like that. (Yes, I did perform a search via the MaplePrimes search before asking this question.) 


Hi guys,

I would like to compute the complex roots of the following equations

u*(BesselJ(0,u)^2 + BesselJ(1,u)^2) = 2 BesselJ(0,u)*BesselJ(1,u)

The function fsolve in Maple gives only 0. I was wondering whether other complex solutions could be obtained as well.

Your help is highly appreciated.



I am solving "Fx=0" for geting "roots:x" using "solve(Fx,x)". Solution is in the form of

"a+sqrt(b)", "a-sqrt(b)"

Here my question is how to extract "a", "b" separately (a, b are complex and very big expressions).


Thank you in advance for your help.




I have to find the root of an equation corresponding to the maximum absolute value. I am using root finding package to get all the roots. But after getting all the roots i am not able to apply abs function. Maple sheet is attached.






Digits := 30



x := proc (t) options operator, arrow; x0*exp(lambda*t) end proc:

phi := proc (t) options operator, arrow; phi0*exp(lambda*t) end proc:

eqm1 := collect(simplify(coeff(expand(diff(x(t), `$`(t, 2))+(2*0)*beta*(diff(x(t), t))+0*x(t)+n*psi*(-v*(phi(t)-phi(t-2*Pi/(n*omega0)))+x(t)-x(t-2*Pi/(n*omega0)))), exp(lambda*t))), {phi0, x0})



eqm2 := collect(simplify(coeff(expand(diff(phi(t), `$`(t, 2))+(2*0)*(diff(phi(t), t))+phi(t)+n*(-v*(phi(t)-phi(t-2*Pi/(n*omega0)))+x(t)-x(t-2*Pi/(n*omega0)))), exp(lambda*t))), {phi0, x0})



mode := simplify(evalc(Re(evalc(subs(lambda = I*Omega, solve(subs(x0 = m*phi0, eqm1), m)))))^2+evalc(Im(evalc(subs(lambda = I*Omega, solve(subs(x0 = m*phi0, eqm1), m)))))^2)



A, b := GenerateMatrix([eqm1, eqm2], [x0, phi0])

A, b := Matrix(2, 2, {(1, 1) = lambda^2+n*psi-n*psi*exp(-2*lambda*Pi/(n*omega0)), (1, 2) = -n*psi*v+n*psi*v*exp(-2*lambda*Pi/(n*omega0)), (2, 1) = n-n*exp(-2*lambda*Pi/(n*omega0)), (2, 2) = -n*v+n*v*exp(-2*lambda*Pi/(n*omega0))+lambda^2+1}), Vector(2, {(1) = 0, (2) = 0})



eq := subs(n = 6, psi = 1000, omega0 = 1.15, v = 0.1e-1, Determinant(A))



zeros := RootFinding:-Analytic(eq, lambda, re = 0 .. 400, im = -200 .. 200)

0.899769545162895563524511282265e-56, 0.813609592584011756247655681635e-1-20.6993361029378520006643410260*I, .242743338419727199544214811606-34.4961764258358768825593120288*I, .440964962950043888796944083291-100.074138054178692973033664525*I, .107710271188082726666762251538-106.954651646879437684160623413*I, 1.12290283496379505456476079030-62.0290638297730162295171014475*I, .879463466045683309032252293625-93.2168861049771086211729407830*I, 2.54860869821265794971735119535-80.1919866273564551209847942490*I, 1.52678990439144770439544731898-86.4450560720567958301493690195*I, 2.62945288424037545703549470125-75.0161229879790946191171617450*I, 1.68779005203728587549371003511-68.8012471850312399391042105550*I, .776570081405504740452992339900-55.1681878011205261920670466495*I, 0.851171007270465178285429398270e-9+1.00000500045406723708450960132*I, 0.851171007270465178285445699470e-9-1.00000500045406723708450960133*I, 0.874874719902730972066854301075e-2-6.89997772561385443312823760560*I, 0.354201863215292148351069041542e-1-13.7998152076043523748759861636*I, .369195444156713173497807954493-41.3921704506707022569621870947*I, .540047057129385026999638567235-48.2843908783769449582520027744*I, .149078330738225743331408017894-27.5982749361891156626731068484*I, .369195444156713173497807954500+41.3921704506707022569621870948*I, .440964962950043888796944083291+100.074138054178692973033664525*I, .107710271188082726666762251538+106.954651646879437684160623413*I, 1.12290283496379505456476079030+62.0290638297730162295171014475*I, .879463466045683309032252293625+93.2168861049771086211729407830*I, 2.54860869821265794971735119535+80.1919866273564551209847942490*I, 1.52678990439144770439544731898+86.4450560720567958301493690195*I, 2.62945288424037545703549470125+75.0161229879790946191171617450*I, 1.68779005203728587549371003511+68.8012471850312399391042105550*I, .776570081405504740452992339900+55.1681878011205261920670466495*I, 0.813609592584011756247655681660e-1+20.6993361029378520006643410260*I, 0.354201863215292148351069041261e-1+13.7998152076043523748759861634*I, 0.874874719902730972066854301075e-2+6.89997772561385443312823760560*I, .540047057129385026999638567235+48.2843908783769449582520027744*I, .242743338419727199544214811602+34.4961764258358768825593120288*I, .149078330738225743331408017894+27.5982749361891156626731068484*I


" 1)"

Error, missing operation

" 1)"




I will be really thankful for the help.



I am having 26th degree polynomial univariate equation , I used Isolate to get the roots. but I am getting some extra roots which are not true they I even tried to substitute those roots in original equation then I got non zero answer instead of getting nearly zero answer.How is it possible??


equation looks like:


Solutions i got:

[t = -4.162501845, t = -2.295186769, t = -1.300314688, t = -.8048430445, t = -0.6596008501e-1, t = -0.4212510777e-1, t = 0.4212510777e-1, t = 0.6596008501e-1, t = .8048430445, t = 1.300314688, t = 2.295186769, t = 4.162501845]

t=4.162501845 give me non zero answer when I substitute it in the equation given above:

I got this answer: 4.750212083*10^39


Hi there,

            Recently, I encountered a problem. I have a function( omega as its variable)  (18)


I tried to find a point where its first derivative equals 0. In this case, Maple returned four solutions. In my

question, both beta, gamma, R4 and C2 >0, I want it to return a real positive solution, the first term

in (19) (i.e. 1/(sqrt(beta *gamma) *1/R4 C2).


I know it is easy to find out the positive real roots in this case. This question seems to make no sense.

However, sometime I came across an expression complicated enough that I cannot tell whether it is real


Is there a approach to find a real positive solution of an symbolic eqution?

Thanks in advance!


                                                                     A University student in BeiHang University, Beijing



how i can calculate roots of the characteristic polynomial equations {dsys and dsys2}
and dsolve them with arbitrary initial condition for differennt amont of m and n?

restart; a := 1; b := 2; Number := 10; q := 1; omega := 0.2e-1

Q1 := besselj(0, xi*b)*(eval(diff(bessely(0, xi*r), r), r = a))-(eval(diff(besselj(0, xi*r), r), r = a))*bessely(0, xi*b):

J := 0:

m := 0:

U1 := (int(r*K1[m]*(diff(K_01[m], r)+K_01[m]/r), r = a .. b))/(int(r*K1[m]^2, r = a .. b)); -1; U2 := -(int(r*K_01[m]*(diff(K1[m], r)), r = a .. b))/(int(r*K_01[m]^2, r = a .. b)); -1; U3 := (int(r^2*omega^2*K_01[m], r = a .. b))/(int(r*K_01[m]^2, r = a .. b))



Q2 := besselj(1, eta*b)*(eval(diff(bessely(1, eta*r), r), r = a))-(eval(diff(besselj(1, eta*r), r), r = a))*bessely(1, eta*b):

E2 := unapply(Q2, eta):

m := 0:

dsys := {diff(S_mn(t), t, t, t)+xi[m]^2*(diff(S_mn(t), t, t))+(-U1*U2+eta__n^2)*(diff(S_mn(t), t))+xi[m]^2*eta__n^2*S_mn(t) = -(2*U2*b_m/(Pi*xi[m])*(-besselj(0, xi[m]*b)/besselj(1, xi[m]*a)))*q+xi[m]^2*U3}; 1; dsolve(dsys)

{S_mn(t) = (3111111111/5000000000000)/(K_01[12]*eta__n^2)+_C1*cos(eta__n*t)+_C2*sin(eta__n*t)+_C3*exp(-xi[12]^2*t)}


dsys2 := {diff(Q_mn(t), t, t, t)+xi[m]^2*(diff(Q_mn(t), t, t))+(-U1*U2+eta__n^2)*(diff(Q_mn(t), t))+xi[m]^2*eta__n^2*Q_mn(t) = -2*besselj(0, xi[m]*b)*U1*U2*b_m*(1-exp(-xi[m]^2*t))/(besselj(1, xi[m]*a)*Pi*xi[m]^3)}; 1; dsolve(dsys2)

{Q_mn(t) = _C1*exp(-xi[12]^2*t)+_C2*sin(eta__n*t)+_C3*cos(eta__n*t)}







Dear all,

I have a question: how to compute the roots of exp(z) = -1 with z in C? 

I tried: 

fsolve( exp(z) = -1, z, complex );

But it only gives one root (0.1671148658e-3+4.934802220*10^9*I) which does not even seem to be correct. I would prefere smth like z_n = I*(2*n-1)*pi or at least multiple roots...

By using

solve(exp(x) = -1, x);

it returns I*Pi.


MATLAB MuPAD gives the desired result:

solve(exp(x) = -1, x)

(PI*I + 2*PI*k*I, k in Z)




when the kummerM function equal to 0?????


-(((beta*eta^2-(1/2)*beta+1)*p^2-(1/2)*beta^3)*KummerM((1/4)*((-beta+2)*p^2-beta^3)/p^2, 1, beta*eta^2)+(1/2)*KummerM((1/4)*((-beta+6)*p^2-beta^3)/p^2, 1, beta*eta^2)*((beta-2)*p^2+beta^3))*exp(-(1/2)*beta*eta^2)/(p^2*beta)=0

how solve this equation unitage beta?

What is the easiest way to ask roots of a polynomial on a finite field. For example asking roots of x^2+xy+y on GF(8)? I was thinking to run a two for on members of GF(8) and ask to check it but I couldn't do it using Galois package or maybe I couldn't use that package. Thanks for any help.


I would like to plot a vertical line each time my function is null and is increasing.

Here an extract of my code:


LignesVerticales=implicitplot(x=To complete, colour=yellow,linestyle=3, thickness=2):

With Roots function, I could obtain the zero-crossings.

With the derative of the functions, I could obtain a vector which gives me when the derivative is positive or not.

I would like now to obtain the list of the zero-crossing values which are increasing but I have difficulties to obtain it. 

By list manipulation, it should be easy to do. 

May you help to plot obtain this list so that I can plot the desired vertical lines?

Thank you for your help

I'm trying to create a routine to perform the test of rational roots , but I'm having some problems. Below is the routine I created :

But the program is only printing " aux = -24 " . I don't know what it can be .

I need to modify my code , but I don't know where. Can someone help me? Thank you!

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