Ha-Nasi, in his book ‘Liber embadorum’ published in Europe in C.E. gave complete solutions of different quadratic equations. In this chapter, you will study quadratic equations, and various ways of finding their roots. You will also see some applications of quadratic equations in daily life situations.
. Quadratic Equations A quadratic equation in the variable x is an equation of the form ax + bx + c = , where a , b , c are real numbers, a . For example, x + x – = is a quadratic equation. Similarly, x – x + = , x – x + = and – x + = are also quadratic equations.
In fact, any equation of the form p ( x ) = , where p ( x ) is a polynomial of degree , is a quadratic equation. But when we write the terms of p ( x ) in descending order of their degrees, then we get the standard form of the equation. That is, ax + bx + c = , a is called the standard form of a quadratic equation . Quadratic equations arise in several situations in the world around us and in different fields of mathematics.
Let us consider a few examples. Example : Represent the following situations mathematically: (i) John and Jivanti together have marbles. Both of them lost marbles each, and the product of the number of marbles they now have is . We would like to find out how many marbles they had to start with.
(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be minus the number of toys produced in a day. On a particular day, the total cost of production was ` . We would like to find out the number of toys produced on that day.
Solution : (i) Let the number