of marbles John had be x . Then the number of marbles Jivanti had = – x (Why?). The number of marbles left with John, when he lost marbles = x – The number of marbles left with Jivanti, when she lost marbles = – x – = – x Therefore, their product = ( x – ) ( – x ) = x – x – + x = – x + x – – x + x – = (Given that product = ) – x + x – = x – x + = Therefore, the number of marbles John had, satisfies the quadratic equation x – x + = which is the required representation of the problem mathematically. (ii) Let the number of toys produced on that day be x .
Therefore, the cost of production (in rupees) of each toy that day = – x So, the total cost of production (in rupees) that day = x ( – x ) x ( – x ) = x – x = – x + x – = x – x + = Therefore, the number of toys produced that day satisfies the quadratic equation x – x + = which is the required representation of the problem mathematically. Example : Check whether the following are quadratic equations: (i) ( x – ) + = x – (ii) x ( x + ) + = ( x + ) ( x – ) (iii) x ( x + ) = x + (iv) ( x + ) = x – Solution : (i) LHS = ( x – ) + = x – x + + = x –