Consider (irreducible) monic polynomials with integer coefficients which satisfy some fixed linear condition $L$ (for example, the coefficient of $x$ is $1,$ or something more complicated). The question is whether the set of real roots of such polynomials is dense in $\mathbb{R}.$ My previous question is for a particular such $L.$ For simple conditions like $a_0 = 1,$ or, indeed, any fixed subset subset of the coefficients fixed, it is known (by the work of S. D. Cohen) that the Galois group of such a polynomial is the full symmetric group, but this is almost certainly completely irrelevant.

Consider (irreducible) monic polynomials with integer coefficients which satisfy some fixed linear condition $L$ (for example, the coefficient of $x$ is $1,$ or something more complicated). The question is whether the set of real roots of such polynomials is dense in $\mathbb{R}.$ My previous question is for a particular such $L.$ For simple conditions like $a_0 = 1,$ or, indeed, any fixed subset subset of the coefficients fixed, it is known (by the work of S. D. Cohen) that the Galois group of such a polynomial is the full symmetric group, but this is almost certainly completely irrelevant.