# Applications Involving Quadratic Equations

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 fulfills 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 travels km 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