Quadratic equations have many applications in the arts and sciences, business, economics, medicine and engineering.

Example:
            A certain negative number added to the square of the number, the result is, what is the number? What is the positive number that fulfils this condition?
Solution:
            Let be a negative number
            By the given condition
                       
                       
            Let,  and
            Using the Quadratic Formula, we have
                       
                       
                       
                                 ,        
                           ,        
Hence, negative number is  and the positive number is.

Example:
            A man travelskm by train and return in car which travel km/h faster. If the total journey takes hours. Find the speed of train and car respectively.
Solution:
                        Let speed of train            km/h
                        Speed of car                    km/h
                        Time taken by the train   hour
                        Time taken by the car      hour
                        Total time                         hours
                       
            Then by the condition
                                   
                       
                       
                         
            Let,  and
            Using the Quadratic Formula, we have
                       
                       
                       
                                 ,        
            Speed of train km/h
            Speed of car    km/h