equation. As you can see, often we need to simplify the given equation before deciding whether it is quadratic or not. EXERCISE . .
Check whether the following are quadratic equations : (i) ( x + ) = ( x – ) (ii) x – x = (– ) ( – x ) (iii) ( x – )( x + ) = ( x – )( x + ) (iv) ( x – )( x + ) = x ( x + ) (v) ( x – )( x – ) = ( x + )( x – ) (vi) x + x + = ( x – ) (vii) ( x + ) = x ( x – ) (viii) x – x – x + = ( x – ) . Represent the following situations in the form of quadratic equations : (i) The area of a rectangular plot is m . The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.
(ii) The product of two consecutive positive integers is . We need to find the integers. (iii) Rohan’s mother is years older than him. The product of their ages (in years) years from now will be .
We would like to find Rohan’s present age. (iv) A train travels a distance of km at a uniform speed. If the speed had been km/h less, then it would have taken hours more to cover the same distance. We need to find the speed of the train.
. Solution of a Quadratic Equation by Factorisation Consider the quadratic equation x – x + = . If we replace x by on the LHS of this equation, we get ( × ) – ( × ) + = = RHS of the equation. We say that is a root of the quadratic equation