Quadratic Equations


Let's glance at an example:


The setup cost for the project to develop a new tank design is 50 thousand dollars. The development cost is a function of time. In other words, the cost increases with time. From previous contracts, the cost function is estimated to be

t2 - 10 t
where t is the time measured in working days. Suppose that a cost analyst has 650 thousand dollars allocated for the project, and he/she wants to know how long before he/she needs to allocate more resources to complete the project?



Let's consider a solution


The total cost for the tank is equal to the sum of the initial cost and the development cost.
t2 - 10t + 50
If $650 thousand has been given, we want to know how much time before more resources need to be allocated?
t2 - 10t + 50 = 650

If we move 650 to the left of the equal sign, this is what we have

t2 - 10t - 600 = 0

To solve the equation above, we just factor the terms as follows:

(t + 20) (t - 30)

The equation yields two answers: t = -20 and t = 30. Since negative time has no physical meaning,

t = 30

is the only valid solution.

Thus, it takes 30 working days before the cost analyst needs to allocate more resources to fund the project.


A few simple facts that you should know


Did you know that the above example has a quadratic equation?

A Quadratic Equation is a polynomial equation in which the highest power of the unknown variable is 2. The most common form of a quadratic equation is an equation where the right hand side is set to zero and the highest exponent of any unknown variable is 2.