Advanced Search

Question: Root finder for the fourth power polynomial

Question:Root finder for the fourth power polynomial

Dkunb 65 Maple 2021
solve rootfinding
April 09 2023
0

Could you help me to solve this problem for the parameter beta?

> 

restart;
> 

e1:= 0.5; e2:=0.2;theta:=5;yeq:=e2;

.5

  

.2

  

5

  

.2

 (1)
> 

f:=(theta*x-1)*(1-x)*(1+beta*x^2)-y;
g:=x/(1+beta*x^2); gs:=unapply(g,x);

(5*x-1)*(1-x)*(beta*x^2+1)-y

  

x/(beta*x^2+1)

  

proc (x) options operator, arrow; x/(beta*x^2+1) end proc

 (2)
> 

fs:=subs(y=yeq,f);

(5*x-1)*(1-x)*(beta*x^2+1)-.2

 (3)
> 

assumptions:=x>1/theta, x<1,beta>0,beta<1,gs(x)>e1;
solve(fs=0,x,useassumptions) assuming assumptions;

1/5 < x, x < 1, 0 < beta, beta < 1, .5 < x/(beta*x^2+1)

  

Warning, solve may not respect assumed property 'real' on 'x/(beta*x^2+1)'.

  

Error, (in type/realcons) too many levels of recursion

  
> 

gs2:=subs(beta=0.6,gs(x));

x/(.6*x^2+1)

 (4)
> 

sol:= solve(subs(beta=0.6,fs=0),x,useassumptions) assuming x>1/theta, x<1;

.2514854589, .9665623271

 (5)
> 

subs(x=sol[1],gs2);

.2422912423

 (6)
> 

 

Download Rootsfind.mw
Please Wait...