TSI Math: More Fun with Quadratic Equations
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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