Majority of Quadratic Equations
There’s a completely different procedure of equation solving that we follow, and
that’s what we’re gonna talk about here. The vast majority of quadratic equations
you will see on the test will have two solutions.
And the quadratic coefficient, the coefficient of x squared, will equal 1, unless a
numerical greatest common factor can be factored out from all three terms. The
vast majority of quadratic equations you’ll see on the test can be solved by the
factoring methods we’ve discussed in the factoring lessons. So if you haven’t seen
those lessons, it will be very helpful to watch those before watching this video,
because we’re going to employ all those factoring strategies here.
We will factor a quadratic to a product of linear binomial. And notice we’ll be doing
this so that this product equals 0. So very important to get things equals to 0 first,
then to do this factoring. Because once we have a product that equals 0 we can
apply this mathematical law, the zero product property. The zero product property
says, if a times b equals zero, if a product of two things equal zero, then either one
is zero or the other is zero.
Before we go on let’s think about this statement for a minute. Keep in mind, that
the “or” that appears in that statement is the mathematical or, not the or of
colloquial language. What’s the distinction of drawing here? The mathematical OR is
an inclusive or. That is it includes the and case. Thus, A = 0 or B = 0 includes three
cases.
It could be that A = 0 and B doesn’t, it could be that B = 0 and A doesn’t, or could
be that they both equal 0 at the same time. You see sometimes in colloquial
language people use the word or to mean the exclusive or. They mean you could do
this Or that, and the implication is that you can’t do both. That’s the exclusive or
that is not how the word or is used in mathematics.
