Algebra 2 Zeros of an Equation
Math-Prof HOME Algebra 2 Table of Contents Ask A Question PREV NEXT

Total Zero
Zeros of an Equation

 

 Someone, somewhere, someday might walk up to you and say ...

 Write an equation where X = 3, X = -2 and X = 0 all make Y = 0.
 
 How would you do it?
 
 Remember when we talked about stuff like:
 

 (X - 2)(X + 5) = 0

 
 We said that if a bunch of stuff multiplied together gave you zero
 one of the things HAD to be equal to zero.
 So:

 X - 2 = 0   or   X + 5 = 0

 
 Then we solved for X

 

 
 So if X = 2 then (X - 2) = 0 and if X = -5 then (X - 5) = 0
 
 Now we have:

 X = 3, X = -2, and X = 0

 being places where Y = 0

 
 So:
  If X = 3 (X - 3) = 0
  If X = -2 (X + 2) = 0
  If X = 0 (X + 0) = 0
 
 So, watch closely ...

 (X - 3)(X + 2)(X + 0) = 0

 
 Multiply out the left side ...

 X3 - X2 - 6X = 0

 
 We're looking for the equation that makes Y = 0
 at those three places. So put in Y for 0
 and we're done!

 X3 - X2 - 6X = Y

 

   copyright 2005 Bruce Kirkpatrick

Math-Prof HOME Algebra 2 Table of Contents Ask A Question PREV NEXT