Quadratic Equations...

[jcmarquez]

1. Why do we factor a quadratic equation before we solve it? I think it is to simplyfy to problem but is that the only reason?.

 

[pka]

By no means is the reason for factoring simplification.
From the axioms for the real field, ℜ, (a)(b)=0 if and only if a=0 or b=0.
Thus x<SUP>2</SUP>−5x+6=0 means (x−2)(x−3)=0 if and only if (x−2)= or (x−3)=0 that is x=2 or x=3.

 

[Denis]

Well, looking at it another way, we TRY to factor a quadratic,
but if that's too difficult, we use the quadratic formula;
so if we're lucky, we've simplified the work...pka??

 

[pka]

Denis, I not sure of your point??
However, the question is about why factor a quadratic?
The fact is any quadratic with real coefficients can be factored into linear products.
(We may have to use complex numbers).
The solutions are found from the linear factors

 

[Denis]

All I'm trying to say is that it takes less time to solve:
x^2 + x - 2 = 0
than it does to solve:
7x^2 + 3x - 39 = 0

We can easily factor the 1st one; no need to do all the steps
required when the quadratic formula is used.

Not important a point anyway!