Solving nonlinear equation inside for loop

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I want to solve for p in the following equation: a1*P^0.5+a2*p+a3*p^1.5=k
if I need to iterate K from 1 to 10000 this is the code:
a1=1.4*10^25;
a2=2.7*10^24;
a3=1.311*10^23;
k=linspace(1,10000,10000);
syms p
for i=1:10000
p(i)=solve((a1*p(i)^0.5)+(a2*p(i))+(a3*p(i)^1.5)==k(i))
end
however I get the following error: Index exceeds the number of array elements (1).
Thank you.
  3 Comments
Kim Ibrahim
Kim Ibrahim on 30 Nov 2021
yes, this equation gives 3 solutions for p when I give k a value at each itertion. the question is i can`t make the dimentions right beause for the 10000 iteration eah give out 3 solutions. That`s the error I get
"Unable to perform assignment because the left and right sides have a different number of elements."

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Accepted Answer

Matt J
Matt J on 30 Nov 2021
Edited: Matt J on 1 Dec 2021
Your equations are really polynomials in p^0.5. Therefore, you can do,
a1=1.4*10^25;
a2=2.7*10^24;
a3=1.311*10^23;
k=linspace(1,10000,10000);
p=cell(1,numel(k));
for i=1:10000
coeffs=[a3,a2,a1,-k(i)]; %polynomial coefficients
p{i}=sqrt(roots(coeffs));
end

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