History of Hindu Mathematics: A Source Book v1.c8.s14.40

v1.c8.s14.40

**Problems involving Solution of Quadratic Equations.** The solution of the quadratic equation has been known in India from the time of Âryabhaṭa I (499). Problems on interest requiring the solution of the quadratic equation have already been mentioned. Mahâvîra and Bhâskara II give many other problems. Mahâvîra divides these problems into two classes: (*i*) those that involve square-roots (*mûla*) and (*ii*) those that involve the square (*varga*) of the unknown. The first type gives a single positive answer, while the second type has two answers corresponding to the two roots of the quadratic. Bhâskara II deals with the first type of problems only in his *pâṭîgaṇita*, the *Lîlâvatî*. The second type of problems, involving the square of the unknown has been treated by him in his *Bîjagaṇita* (algebra). The following examples will illustrate the nature and scope of such problems: