Does the US Supreme Court have any authority or authority to require that a potential juror be questioned about racial prejudice?

Reviewing its decisions in Aldridge v. United States (1931) 283 U.S. 308, 51 S.Ct. 470, 75 L.Ed. 1054 (the "seminal case requiring inquiry as to racial prejudice," Mu'Min v. Virginia, supra, 500 U.S. at p. ----, 111 S.Ct. at p. 1905) and Ham v. South Carolina (1973) 409 U.S. 524, 93 S.Ct. 848, 35 L.Ed.2d 46, each of which required that some inquiry be made about racial prejudice in light of the "special circumstances" presented, the Mu'Min court recalled that its holding was "that the subject of possible racial bias be 'covered' by the questioning of the trial court in the course of its examination of potential jurors, but we were careful not to specify the particulars by which this could be done. We did not, for instance, require questioning of individual jurors about facts or experiences that might have led to racial bias." (500 U.S. at p. ----, 111 S.Ct. at p. 1908.)