Hi class, I would like to talk about two
problems in your complex numbers and
quadratic equations. I know some of you
already have this done and did it
correctly, but some of you still want to
see how I do it.
So here it is the first problem would be
x squared plus X plus 1 equals 0 now for
any quadratic equation we have many ways
to do it either by factoring, completing
the square, or using the quadratic formula
For this problem we see that this is
not factorable. So it's not the option. So
we have to use a quadratic formula. So
let's review what is a quadratic formula
we have Ax squared plus BX plus C equals
0 and standard equations now a is a
coefficient of x squared B is the
coefficient of the X and C is the
constant then these solute this equation
half the solution is negative B plus and
minus square root of 4 sorry let me do
this again oops b square minus 4ac all
over 2a ok so we're going to use this
formulas to solve these equations so the
solution to this equation is negative B
which is negative 1 plus and minus B
squared so 1 square minus 4 A C all
over 2a
technically we just plug in the number
now let's simplify this I have negative
one plus and minus one minus 4 all over
2
ok so we know that the square root of
negative 3 is the square root of
negative 1 times 3 which is "i" times
square root of 3 so then we can go back
in here and start to simplify this ok so
here is a solution now if the question
have two boxes for you to plug in
doesn't mean you have one X I call this
X_1 is negative 1 plus I square root of
3 all over 2 and the second solution to
this equation is negative 1 minus "i"
square root of 3 over 2 that is one way
to write it another way to write is you
have X 1 is negative 1/2 plus I square
root of 3 over 2 or this one you have
negative 1/2 minus I square root of 3 ok
All right so this is the first example.
