MATLAB: How to represent the roots of a polynomial on a graph

polynomial roots on graphs

how to represent the roots of a polynomial on a graph?

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p=[1 2 3 4 5]; % your polynomial x^4+2x^3+3x^2+4x+5
r=roots(p)
scatter(real(r),imag(r),'filled','red')

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MATLAB: Real Roots of a Polynomial

Use 'roots' to find the roots of polynomials.

 r = roots([1,7,-8,5,1]); % Get all the roots
 r = r(imag(r)==0); % Save only the real roots

The 'isreal' function is true only if All elements of a vector are real, so it isn't appropriate for sorting out the real roots.

A polynomial with all real coefficients such as yours cannot have an odd number of complex roots. They must occur in conjugate pairs. As you see, in your particular polynomial there are just two complex roots, which are conjugates of one another.

MATLAB: Find roots

The key to this problem is that there is one root in each interval [n*pi,(n+1)*pi]. I'm going to assume that L > 1, otherwise the region near the origin is a special case.

function beta = find_beta(L,nRoots)
f = @(x) x*cot(x)+L-1;
beta = zeros(nRoots,1);
% A small offset is needed to avoid the asymptotes.
smallOffset = 1e-12;
for i=1:nRoots
    beta(i) = fzero(f,[i*pi+smallOffset (i+1)*pi-smallOffset]);
end

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Related Solutions

MATLAB: Real Roots of a Polynomial

MATLAB: Find roots

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