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um so let me i'll just go over this one
just to help you guys out it just says
find the zeros and then determine
multiplicity to find the zeros of course
the first thing we're going to do is set
up our function to zero
therefore we have t to the fifth minus
six t cubed
plus nine t
then the next thing we're going to do is
we're going to um
determine our gcf well we can see that
each one of these terms
shares a t it's all factored out of t
thank you
so i have to
factor out a t times
t to the fourth minus t squared plus
nine
now i'm sorry let's say
sixty right
six t squared all right so now i need to
factor this well i gave you that
worksheet remember on perfect square
trinomials a squared minus two times or
a squared or plus or minus two two a b
plus b squared well no notice that john
t to this fourth is a squared term nine
is a squared term
and
the negative six t squared is two times
a times t already times b so therefore i
can factor this as zero equals t
times t squared minus three times t
squared minus three
now again
yes that's the factored form you guys
can do the x if you want to do the x and
you can convert this to c squared if you
want to uh but now we have t squared
minus r sorry t squared minus 3 times t
squared minus 3 so we have 0 equals t
times t squared minus 3
squared
right
all right so we're going to determine um
let's go and first find the zero so i
apply zero product property
t equals zero
and t squared minus three
squared equals 0.
so now in this case i solve well i
already solved t equals 0. so that's
easy here i'm going to have to apply my
inverse operations so i'll take the
square root of both sides
then i'm left with
t squared minus three equals square root
of zero is just zero
then i add three
t squared equals a positive three
take the square root take the square
root
t
equals plus or minus the square root of
three now those are two different zeros
right let's look again at the
multiplicity of their factor the
multiplicity of their factor is a what
we'll keep two so you could say that
these two i'm not going to write
multiplicity i'll say
m
multiplicity here is two or even here we
have a multiplicity that was one right
because remember t can be written as t
minus zero
right so therefore this multiplicity is
equal to one
so therefore the graph crosses at t
equals zero
and then touches
at
plus or minus the square root of 3.
there okay go
good
make sense
see you around
or maybe
get good pass
all right um
