Using nlsolve for roots of Legendre Polynomials in terms of RadauIIA method

New to Julia
,
1

Hi,

I need to find root for Legendre polynomials in terms of the RadauIIA method

using ClassicalOrthogonalPolynomials, NLsolve

function P(x, n)
    return legendrep(n, x)
end

function radc(x, s)
    v = 2 * x - 1
    return P(v, s) - P(v, s-1)
end

s = 3

k = zeros(s)

function radc!(fk, k)
    fk .= radc(k, s)
  end

c = nlsolve(radc!, k)

nlsolve is difficult to use. I used this same method of nlsolve for something else and it worked, but not for the above.

Please help me.
Thanks