# I'm getting error as "First argument must be scalar" while finding roots of a 8 degree poynomial

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Apurva Suman on 3 Dec 2021
Commented: Matt J on 3 Dec 2021
root([2*A*B*K^2 - B^2*K^2 - A^2*K^2, - 4*A*B*K^2*R + 2*B^2*K^2*R + 2*A^2*K^2*R + 2*B*C*K^2 - 2*A*C*K^2, - 2*B*C*K^2*R + 2*A*C*K^2*R + 2*A*B*K^2*R^2 - B^2*K^2*R^2 - A^2*K^2*R^2 - C^2*K^2, -1, + 5*R, - 10*R^2, + 10*R^3, -5*R^4, R^5])
%this is what i'm doing , actually i needed all real roots in terms of variables, but i'm getting error that says first argument must be scalar

Matt J on 3 Dec 2021
Edited: Matt J on 3 Dec 2021
You have 2 problems.
First, you are trying to find analytical expressions for the roots of an 8-degree polynomial, which is mathematically impossible.
Second, you are confusing the syntaxes of the two different commands root() and roots(). You can find the roots of an 8-degree polynomial with the roots() command, but not with symbolic input variables.
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Matt J on 3 Dec 2021
x will have a very small value, upto x^3 its not neglibile but terms with power above than that can be neglected
But all of the polynomial coefficientsterms below x^5 depend on R only:
syms K A B C x R
P= ( ( (R^2)*K*( A - B - (C/R*(1- x)) )*((x^3)/(1-x)) )^2 ) - R*(1- x) ;
P=simplify( simplifyFraction(P*(x - 1)^2),'Steps',5);
Coeffs=coeffs(P,x,'All');
Coeffs(end-5:end)
ans = 