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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