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Let $\mathcal{E}_d^{(s)}$ denote the set of coefficient vectors$(a_1,\dots,a_d)\in \mathbb{R}^d$ of contractive polynomials$x^d+a_1x^{d-1}+\dots+a_d\in \mathbb{R}[x]$ that have exactly $s$ pairs ofcomplex conjugate roots and let $v_d^{(s)}=\lambda_d(\mathcal{E}_d^{(s)})$ beits ($d$-dimensional) Lebesgue measure. We settle the instance $s=1$ of aconjecture by Akiyama and Peth\H{o}, stating that the ratio$v_d^{(s)}/v_d^{(0)}$ is an integer for all $d\ge 2s.$ Moreover we establishthe surprisingly simple formula $v_d^{(1)}/v_d^{(0)} = (P_d(3)-2d-1)/4,$ where$P_d(x)$ are the Legendre polynomials.

A number theoretic problem on the distribution of polynomials with bounded roots