# TSI Math: More Fun with Quadratic Equations

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

 Intermediate Algebra and Functions Quadratic and Other Polynomial Expressions, Equations, and Functions Mathematics and Statistics Assessment Quadratic and Other Polynomial Expressions, and Functions Product Type TSI TSI Mathematics and Statistics AssessmentTSI MathTSI Mathematics TSI Math Intermediate Algebra and Functions TSI Mathematics Intermediate Algebra and Functions Test Prep TSI

### 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

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of negative three from each term shines a light on

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

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

00:40

out gets us was that three z squared minus five

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z minus two zero Well the negative three casts an

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ominous shadow on the tri no menial three z squared

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minus five c minus to scare it away by dividing

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the entire equation by negative three including that zero on

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the far right If only sharks were afraid of division

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

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here rewrite the middle term of trento meal by identifying

01:01

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

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three which is negative six on the end got to

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find them also to be ableto add two negative five

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

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well negative six times one is negative six and the

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negative six plus ones Negative five So negative five z

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can be re written as yes negative six z plus

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

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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

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the first two terms the last two terms and apology

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

01:38

this three z squared minus sixty plus z minus two

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And we can pull three z out of this thing

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here while realizing z minus two is a factor of

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both terms Like finding a beautiful pearl inside of a

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clam factor that by no meal out and that gets

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us well z minus two quantity three z plus one

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zero and for the entire equation equals zero Either one

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or both of the factors must equals zero right So

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we saw for zeon Both of them start just by

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setting z minus two Equal to zero and miles equals

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two Beautiful Do the same thing with second factor three

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z plus one and well three z then is negative

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one so we divide three on both sides so z

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then is negative a third with the grace of a

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mermaid or a large man Iti we recover the solutions

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off Negative ninety square plus fifteen z plus six equals

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zero which are z equals two and c equals negative

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