Here are the methods we have learned so far to solve quadratic equations. We
first started by reviewing factoring. Then we looked at the root method, and
finally, we completed the square. Factoring is perhaps the easiest method if we
can factor a quadratic equation. If we can't factor it, then we'll want to use
one of these two approaches in order to get our solution. And if none of these
three methods will work, we have one last method that will always work. That
method is the quadratic formula. There are some advantages and disadvantages to
this method. Let's see what they are. For any equation written in this form, we
can find the solutions to it by doing negative b plus or minus the square root
of b squared minus 4ac, all divided by 2a. This is our quadratic formula and it
only requires that we know the values of a, b, and c. a is the coefficient of
the x squared term, b is the coefficient of the x term, and c would be the
constant term. I mentioned the pros and cons of this quadratic formula. Well,
the pro is that it can solve any quadratic equation, so long as we have the a,
b, and c, and the left-hand side is set equal to 0. We could also have the
equation reversed, the left-hand side could be 0 and the right-hand side could
be this. For the cons, it's actually very easy to make a sign error in two
places. Here, we need to take the negative value of b, so if to change the
sign. The other place that we might make a sign error is underneath the
radical. b squared should always end up being a positive number, and then we
have minus 4ac. Now, depending on the values of a and c, this second term might
end up being positive or it might stay negative. You'll want to pay close
attention to how many negative signs you have here to determine this number.
And finally, another drawback to the quadratic formula is that we have to
simplify. We'll need to simplify this radical. And then we'll also need to
simplify this fraction if we can. Sometimes, this result will end up being the
integers, and sometimes, it will end up being fractions. Keep in mind that we
could get imaginary solutions if we have a negative radical here.
