TSI Math: More Fun with Quadratic Equations

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

Intermediate Algebra and FunctionsQuadratic and Other Polynomial Expressions, Equations, and Functions
Mathematics and Statistics AssessmentQuadratic and Other Polynomial Expressions, and Functions
Product TypeTSI
TSIMathematics and Statistics Assessment
TSI Math
TSI Mathematics
TSI MathIntermediate Algebra and Functions
TSI MathematicsIntermediate Algebra and Functions
Test PrepTSI

Transcript

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