By the construction of suitable graphs and the determination of their chromatic polynomials, we resolve two open questions concerning real chromatic roots. First we exhibit graphs for which the Beraha number (Formula presented.) is a chromatic root. As it was previously known that no other noninteger Beraha number is a chromatic root, this completes the determination of precisely which Beraha numbers can be chromatic roots. Next we construct an infinite family of 3-connected graphs such that for any (Formula presented.), there is a member of the family with (Formula presented.) as a chromatic root of multiplicity at least (Formula presented.). The former resolves a question of Salas and Sokal and the latter a question of Dong and Koh.