History of Hindu Mathematics: A Source Book v2.c17.s8.123

v2.c17.s8.123

Following Pṛthûdakasvâmî let us take in *Example* 1 the residue of the revolution of the sun to be x² + 2; then by the question $10(x - 1) + 2 = x² + 1,$ $or x² - 10x = - 9.$ In *Example* 2, put 4x for the residue of the exceeding months; then $(x - 3)² = 4x,$ $or x² - 10x = - 9.$ Now, by the second rule of Brahmagupta, retaining both the signs of the radical, we get $x = 5 ± √(25 - 9) = 9 or 1.$ As shown by Pṛthûdakasvâmî, the first value is taken for *Example* 1 and second value for *Example* 2. Thus it appears that Brahmagupta uses sometimes the positive and at other times the negative sign with the radical. Hence it seems that Brahmagupta knew that a quadratic equation has two roots, though from considerations of utility in his problems, he retains only one of them.