# 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 Assessment TSI Math TSI Mathematics |

TSI Math | Intermediate Algebra and Functions |

TSI Mathematics | Intermediate Algebra and Functions |

Test Prep | TSI |

### Transcript

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

heads or hands in tow dark holes where squid like

creatures could be lurking Avoid tangling with the easy ones

in particular Alright so pulling out a g c f

of negative three from each term shines a light on

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

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

out gets us was that three z squared minus five

z minus two zero Well the negative three casts an

ominous shadow on the tri no menial three z squared

minus five c minus to scare it away by dividing

the entire equation by negative three including that zero on

the far right If only sharks were afraid of division

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

here rewrite the middle term of trento meal by identifying

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

three which is negative six on the end got to

find them also to be ableto add two negative five

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

well negative six times one is negative six and the

negative six plus ones Negative five So negative five z

can be re written as yes negative six z plus

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

of nowhere like this and problems seems to be the

key for a whole lot of these questions If you

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

of points on this exam Okay so moving on group

the first two terms the last two terms and apology

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

this three z squared minus sixty plus z minus two

And we can pull three z out of this thing

here while realizing z minus two is a factor of

both terms Like finding a beautiful pearl inside of a

clam factor that by no meal out and that gets

us well z minus two quantity three z plus one

zero and for the entire equation equals zero Either one

or both of the factors must equals zero right So

we saw for zeon Both of them start just by

setting z minus two Equal to zero and miles equals

two Beautiful Do the same thing with second factor three

z plus one and well three z then is negative

one so we divide three on both sides so z

then is negative a third with the grace of a

mermaid or a large man Iti we recover the solutions

off Negative ninety square plus fifteen z plus six equals

zero which are z equals two and c equals negative

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