Vyasa to the rescue

Satyavati's two sons both died childless but Bhishma refused to revoke his vow of Brahmacharya. There was, thus, no heir apparent to the throne of Hastinapura. Satyavati then remembered the son she had had with Parasura, a wandering minstrel  and sent out to him.

Vyasa, her son, came from the forests. He was a hermit, covered with ashes and definitely not a sight for the courtly queens of Hastinapura. Yet, Satyavati called Vyasa and asked him to father children upon the wives of his half-brother, Vichitravirya.

The first month, Vyasa was to live with Ambika. When Vyasa entered her chambers, Ambika was so scared of the dirty, unwashed hermit that she closed her eyes even as she yielded to him. The son born to her, Dhritarashtra, was accordingly born blind.

The second month, Vyasa stayed in Ambalika's chambers. Ambalika turned ashen at the thought of cohabiting with the hermit. The son born to her of Vyasa, Pandu, was born pale-skinned.

When Satyavati saw her two grandchildren, one blind and the other with melanoma, she was not pleased. She ordered Ambika to bear another child. Ambika, however, had had enough of the dirty and uncouth sage. She sent her maidservant in her stead. The maidservant, a hearty girl of a bountiful nature, had no qualms with the unwashed sage. She bore of the encounter, a healthy male child. They called him Vidura.

Thus, O King, was the line of Bharatas - the line of Yayati and Puru continued .