Expert: Paul Klarreich - 10/11/2006

Question
to solve the quadratic equation y= x^ -6x +8 =0
why is there 2 equal values?
when factoring i get an answer of 4 solving using the quadratic equation i also get an answer of 4. I am not sure why.

Answer
pam nicholls Asks in Category Advanced Math ...
 
Subject:  quadratic equations-studying algebra
Private:  no
 
Question:  to solve the quadratic equation y= x^ -6x +8 =0
why is there 2 equal values?
when factoring i get an answer of 4 solving using the quadratic equation i also get an answer of

4. I am not sure why.
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You wrote:
When factoring i get an answer of 4

AND x = 2, you meant to say, right?  Don't forget there are two roots, which may be equal, but are not here.

You wrote:
solving using the quadratic equation i also get an answer of 4

AND x = 2, you meant to say, right?


I am not sure why.

First, there are always two solutions to a quadratic equation.  So when you factor:

x^ - 6x + 8 = 0    <<<  BTW, the 'y' is superfluous and applied to a different kind of example, a graph of a quadratic FUNCTION, not an equation.

You get:

(x - 4)(x - 2) = 0

Set each factor equal to zero and you get your two roots.  SOMETIMES, the two roots are the same number (not this time) and we call that a DOUBLE root.

As to why you get the same two roots using the quadratic formula, which comes down to:
   6 +- sqrt(4)
x = ------------
       2

   6 +- 2
x = -------
      2
Which becomes:

   6 + 2
x = ----- = 4
     2

OR

   6 - 2
x = ----- = 2
     2

It does not matter which method you use -- you should get the same results either way, ASSUMING THAT THE EQUATION CAN BE FACTORED.  Most of them cannot.  When you study quadratic equations by factoring, your teacher picks out the few that can, and that's your homework.