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Description:

Which of the following are the solutions to the equation -9z² + 15z + 6 = 0?


Transcript

00:02

All right sy mash bumpers Another question for you Here

00:04

we go Which of the following are the solutions to

00:06

the equation Negative ninety squared plus fifteen year plus six

00:10

Zero hello quadratic ce All right well let's grab historical

00:18

and dive right into solving This is puffy here while

00:21

exploring the depths of the ocean We don't recommend sticking

00:24

heads or hands in tow dark holes where squid like

00:26

creatures could be lurking Avoid tangling with the easy ones

00:29

in particular Alright so pulling out a g c f

00:32

of negative three from each term shines a light on

00:35

how to proceed and you'll scare a few fish by

00:37

doing that so let's do this thing negative three pulled

00:40

out gets us was that three z squared minus five

00:42

z minus two zero Well the negative three casts an

00:45

ominous shadow on the tri no menial three z squared

00:48

minus five c minus to scare it away by dividing

00:51

the entire equation by negative three including that zero on

00:54

the far right If only sharks were afraid of division

00:56

to all right so that's what it gives us right

00:58

here rewrite the middle term of trento meal by identifying

01:01

factors of well it's a negative to there and times

01:04

three which is negative six on the end got to

01:07

find them also to be ableto add two negative five

01:09

so well let's see negative six and one work because

01:13

well negative six times one is negative six and the

01:15

negative six plus ones Negative five So negative five z

01:17

can be re written as yes negative six z plus

01:21

z and notice Pulling out the z's in the middle

01:24

of nowhere like this and problems seems to be the

01:26

key for a whole lot of these questions If you

01:28

could do it fluidly well you'll score a whole bunch

01:31

of points on this exam Okay so moving on group

01:33

the first two terms the last two terms and apology

01:35

cf out of each group So we'll group him like

01:38

this three z squared minus sixty plus z minus two

01:41

And we can pull three z out of this thing

01:43

here while realizing z minus two is a factor of

01:46

both terms Like finding a beautiful pearl inside of a

01:48

clam factor that by no meal out and that gets

01:51

us well z minus two quantity three z plus one

01:54

zero and for the entire equation equals zero Either one

01:57

or both of the factors must equals zero right So

02:00

we saw for zeon Both of them start just by

02:03

setting z minus two Equal to zero and miles equals

02:06

two Beautiful Do the same thing with second factor three

02:09

z plus one and well three z then is negative

02:13

one so we divide three on both sides so z

02:16

then is negative a third with the grace of a

02:18

mermaid or a large man Iti we recover the solutions

02:21

off Negative ninety square plus fifteen z plus six equals

02:24

zero which are z equals two and c equals negative

02:28

A third it's just that's it We're done We're shmoop 00:02:33.863 --> [endTime] what

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