I have this problem- lets say I have a polynomial which has real parameters as coefficients and I'm looking for the scope of the parameters where the polynomial can have real roots. e.g $x^2+kx+k$ we know that for $0<=k<=4$ we won't have real roots. Is there any algorithm for finding the scope of k for higher order polynomials? Thanks
edit: I think this can be found by Samuelson's inequality , solving what is in the square root will give the bounds. How can this be done to a polynomial with more than one varaiable?