Quadratic equation

[Yuseph]

Yo guys,

Im at the quadratic equation chapter now
Look. So far i had been taught that when you had found x its value were the same for all x on the equations
But now with this new chapter it seems that we can use the same letter to refer to two different values.
So my first question would be... what ??!
My 2nd question is, since im new to all this, in what practical situation could this be used ?

 

[R.M.]

Yes, a variable can represent 2 different values, but not simultaneously. Take a simple quadratic: x² = 9. In words, this says "what number times itself equals 9?". There are 2 values of x that satisfy that: x = 3, or x = -3.

x² - x - 6 = 0. The 2 values of that satisfy the equation are 3 and -2.
3² - 3 - 6 = 9 - 3 - 6 = 0
(-2)² - (-2) - 6 = 4 +2 - 6 = 0

Notice that you either plug in 3, OR -2, but not both simultaneously.

Practical situation:
A baseball is hit high into the air. While the ball is rising, there is a certain point in time that it is 100 feet off the ground. While the ball is falling, there is a later point in time where the ball has returned to 100 feet off the ground. Think of each point in time as an 'x-value', and each height as a 'y-value'. So you have 2 different times (x's) that give the same height (y).