# Applications Involving Quadratic Equations

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

__Example__:

A certain negative number is added to the square of the number, and 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, the negative number is and the positive number is .

__Example__:

A man travels km by train and returns in a car which travels km/h faster. If the total journey takes hours, find the speed of the train and car respectively.

__Solution__:

Let the speed of the train km/h.

Speed of car km/h

Time taken by the train hours

Time taken by the car hours

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