The second method we wish the look at solving
quadratic equations is a method that will
tell you whether you have solutions for every
quadratic equation so it is a fail-safe method
the one thing about it is that there are some
technical and somewhat time consuming complications
connected with it and that’s why people
often try not to use it is they can do solving
by factoring easier. Anyways the first thing
you need to do in solving your quadratic equation
just as you did solving by factoring is to
put the quadratic equation in standard form.
So all non-zero terms are to the left side
of the equals sign and just zero is on the
right side.
In the general equation that you see
on the page on the screen you have your quadratic
equation is of the form ax squared plus bx
plus c equals 0. Here when you are doing an
actual problem a, b, and c are standing in
for real numbers and it would be any real
number could be substituted in for the a,
b, and c in the format and those numbers are
called the coefficients of the equation. Once
you have the problem set up so it’s in standard
form and you’ve identified what a, b, and
c are, you can directly calculate the solutions
to this equation by substituting a, b, and
c in the formula give which is called the
quadratic formula.
Your solutions are x equals negative
b plus the square root of b squared minus
4ac over 2a and –b minus the square root
of b squared minus 4ac over 2a. So we’d
like to do an example to show how to apply
this our problem is x squared minus 18x plus
60 equals 0. So the first thing we do is we
identify what a is and what b is and what
c is and we have a is 1, b is -18 and c is
60. This first thing you should do in the
calculation is you should calculate b squared
minus 4ac as is noted on the screen. If you
calculate this value and your answer is negative
you’ll have a negative number underneath
the square root sign and that will not give
you a real number answer.
3:01 So you could just stop there and say
there’s no solutions. So we’ve shown that
we’ll calculate b squared minus 4ac for
this problem and it will be a negative 18
squared minus 4 times 1 times 60. That gives
you 324 minus 240 is 84 so that’s a positive
number. So we can continue on and try to complete
the problem. Take the square root of 84 because
we are doing the successive computation don’t
round that yet write down all the digits that
come out from your calculator. Then the two
solutions will be negative b plus 9.16515139
divided by 2a and negative b minus 9.16515139
divided by 2a. We now substitute the proper
values into the problem for b and for a and
we do the computation and we get our answer
and we finally round at the last moment and
we get 13.58 or 4.42. The next lecture will
be a bit about rounding, so please listen
and read that one.
Subtitles by the Amara.org community
