MATLAB: 4th degree equations

nonlinear algebraic equation

Hi, can anyone help me with this problem? We need the smallest positive real root of this equation
a*x^4+b*x^3+c*x^2+d*x+e=0,
where a>0, b<0, c>0, d<0 and e>0. As Descartes said, in that case this equation has at least 2 positive real roots.
Thank you for your attention.

Best Answer

r = roots([a,b,c,d,e]);
r(imag(r)~=0) = [];  %remove complex
r(r <= 0) = [];  %remove non-positive
min(r)  %now it is the smallest positive real root
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