Solving nonlinear equation inside for loop

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.

[Kim Ibrahim]

when I solve it outside the for loop for one value of K it gives me 1 solution; however i'm expecting three soutions

[Dyuman Joshi]

You are expecting 3 solutions for each p and k, right?

[Kim Ibrahim]

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."

Answer 1

[Matt J]

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

[Kim Ibrahim]

Thank you so much, the cell array helped.