Algebra problem , trinomial / help please.

[frkelly74]

.....2
12y -5y -2 = 0

We home school and our middle daughter has run into an equation that we can't solve to match the answer in the book.

it should read 12y squared - 5y -2 =0

I know there are some who understand the correct way to factor this out and might offer us some instruction on this.

thank you

[btroj]

(12y-5)y-2=0. Is what I would say. What does the book say?

[Wag]

Try this page and see what you get.

http://www.algebrahelp.com/lessons/factoring/trinomial/pg2.htm

--Wag--

[frkelly74]

the book gives two solutions , y=1/3 and y=-1/4

I got +/- 2/7 when I tried it.

[Live2Ride]

12y^2 -5y-2= 0 can be factored to (4y + 1) (3y -2) = 0 that would allow for two answers of y = -1/4 and y = 2/3.

[southpaw]

12y^2 - 5y -2 = 0

(4y+1)(3y-2)=0

4y+1=0
4y= -1
y= -1/4

3y-2=0
3y=2
y=2/3

y= -1/4, 2/3

Thanks for the flash back. Had to rack my brain a little...

Jerry Jr.

[Baja_Traveler]

Gawd I remember those - I was a math flunky in school, never could understand that stuff.

And here I am in my mid 50's and have yet to run across a real life reason to know that. Geometry yes and even a little Trig here and there, but Algebra no...

[jonp]

I came out with y^2 = 1/72 on my first try. DOH!:killingpc

[frkelly74]

Thanks ALOT! My daughter is moving on thanks to you. She says she especially agrees with baja traveler though.

So if I understand it , because the equation needs to be equal to zero one of the terms multiplied must be zero, so therefore it can have two solutions depending on which term you assume to be zero. Actually that does make sense to me.

[Echo]

Great ZOT! Decades ago, it would have been easy! I'm glad for the stimulus, and refreshing the memory.
Great Zot...

[Hardcast416taylor]

I had a few touches of trig math in H.S. and again in college for first year math requirement. When I entered the Pipefitter/Steamfitter/Plumber apprenticeship program that had math requirements imagine my shock to see that these included PLANE & SOLID TRIG CLASSES! I believe those classes are the reason I am bald today for all the hair pulling over them. I managed to pass both classes with low C grades, but I passed! To this day some 40+ years later I have yet to use any of those Trig formulas - simple Algebra and some Geometry formulas yes.Robert

[ACrowe25]

I teach algebra at the university to pay for my schooling as a chemist.

If I read it correctly, it is just a quadratic equation (highest power 2... Ax2 + bx + c). If you can't factor by guess and check (.....)(.....) you can always use the quadratic formula. If guess/check worked... And you just couldn't see it the QF will give the same answer so no worries.

QF can be found in any math text.

[ACrowe25]

As southpaw showed it was factored by guess and check. Just wanted to point out going to the QF (in terms of a time crunch if your having a brain fart is NEVER WRONG.

[ACrowe25]

Thanks ALOT! My daughter is moving on thanks to you. She says she especially agrees with baja traveler though.

So if I understand it , because the equation needs to be equal to zero one of the terms multiplied must be zero, so therefore it can have two solutions depending on which term you assume to be zero. Actually that does make sense to me.

GREAT question...

So it's basically a trick played by mathematicians. Yes it must always be set to zero. I believe it is called the zeroth property? Check the text.

But now think about it... 9 * 0 is 0. 273292* 0 is zero.

Therefore if our answer is zero... Just one term needs to be equal to zero as if it is... The entire answer is zero. Get it?

So that way when factored (by guess and check above) we can set each term equal to zero because if that single term is zero it does not matter what the other term is as we are being multiple... Therefore the answer will be zero and the statement is true.

[45 2.1]

There is only one variable...y.... The equation has only one answer... 2/3..... Insert anything that you think is the answer back in the original equation for proof.

[stephenj]

Here is a place everyone should know about ... if you have high speed internet at least.

Www.khanacademy.org

A most helpful place ... basicly a free class room .
Basic threw advanced mathmatics. And many other subjectsy

[GL49]

Umm….. one variable,two answers.
y= -1/4
y=2/3
Southpaw is correct

[fouronesix]

Really should be a very simple type of equation to solve for value of y. But seems like there is an error (typo or missing paren's or missing exponent) in the original which fouls up attempts at solution. Re-check to make sure there isn't an error in the original format. No telling what can happen mathematically with typos, misprints or missing paren's or even missing exponents. :)

By adding (guessing at) segregation paren's, the simplest solution might be y=2/7. However math doesn't mix well with typos, by guess or by golly... so who knows ?

Likely it is missing an exponent (y). Then it becomes standard factoring of a polynomial.. in this case a trinomial. The easiest and maybe best way to check your method and work would be to use one of the online algebra tutorials that has been suggested.

OK, I did a search for some tutorials on this. Some of the stuff I saw during the search was junk. :(

I however did find this and it is the method I learned 48+ years ago and IMO is the best.

Solution for 12x^2-5x-2=0 equation:

Simplifying
12x2 + -5x + -2 = 0

Reorder the terms:
-2 + -5x + 12x2 = 0

Solving
-2 + -5x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -4x)(2 + -3x) = 0

Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = 0 + 1
-4x = 0 + 1

Combine like terms: 0 + 1 = 1
-4x = 1

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25
Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-0.25, 0.6666666667}

[felix]

Southpaw is correct ONLY if the X axis were involved also. His case would have X=0 as the second equation in combination with the first equation. When there is only one equation, the X axis (and ALL others) would be assumed to equal zero. So, algebra speaking, Bobby (45/2.1) is correct.

The trouble with math is just what was shown. Math represents curves, or better yet, relationships based upon nature which cannot be digitally represented accurately. The field of numerical analysis (higher math) takes these errors into account, but only plays with the digital numbers, and not the functions of nature.

I guess this is why the Doctor of Philosophy came into being for the math field(s). Just another foreign language, so to speak. ... felix

[uscra112]

southpaw is correct only if the x axis were involved also. His case would have x=0 as the second equation in combination with the first equation. When there is only one equation, the x axis (and all others) would be assumed to equal zero. So, algebra speaking, bobby (45/2.1) is correct.



The trouble with math is just what was shown. Math represents curves, or better yet, relationships based upon nature which cannot be digitally represented accurately. The field of numerical analysis (higher math) takes these errors into account, but only plays with the digital numbers, and not the functions of nature.

I guess this is why the doctor of philosophy came into being for the math field(s). Just another foreign language, so to speak. ... Felix

huh ?

[Beerd]

93115

[GL49]

Double "HUH"

[ACrowe25]

I disagree... The problem represents and equation not a function of a line. In my opinion solving for zeros as shown previously is correct. It is not written as f(x).

Maybe I'm not interpreting the question correctly but being that my answers match with the book I am.

[MtGun44]

Math is a tool. You need to learn math to develop tools to solve problems
in life. If you never work on anything where math beyond addition, subtraction
and division are necessary, you may not need to go past the first introductory
algebra class, but it DOES help develop good thinking skills in general.

I have been doing engineering since 1973 and math is a major part of what
I do. For many, not so much. I used to teach math to adults and
really enjoyed giving my students BUCKETS of word problems. Got huge
amounts of groans, but I pointed out that it was pretty unlikely that anyone
may every give you a particular algebra problem to solve in life - but that
it was HIGHLY likely that you would run into a real world problem where
algebra was the way to get the answer and translating from a WORD PROBLEM
to an algebra problem was a critical real world skill. Algebra without learning any
way to get a real world problem set up as the correct algebra problem is
not too useful. So, I did tons of word problems and we spent a great deal
of time learning how to translate English into Math. Really.

Wound out taking a small group of students all the way thru practical
applications of trigonometry - which is different than the purely mathematical
look at trig that is given in many course that are aimed at prep to
higher math. Practical trig is actually pretty useful, and amazingly easy
to learn in a short time, if taught well.

Bill

[Love Life]

Why is everybody typing in a foreign language on this thread?

[btroj]

Bill, what most people can't see is that life is full of story problems.

If I want t know how many 200 gr bullets I can get from a 5 gallon bucket of wheel weights I use math to solve a story problem. 5 gallons is about 175 pounds of WW. Smelted I get 80 percent recovery so .8 times 175. Multiply that by 7000 gr per pound, divide by 200, bullet weight, and get the number of bullets.

We don't always see math or algebra being present in our lives but it sure as heck is there. All day, every day.

[MtGun44]

btroj

That was what I was teaching my students. Some of them even got it. :bigsmyl2:

Bill

[btroj]

I may not be an engineer but as a pharmacist I see this quite easily. I see t more so with my sophomore engineering student daughter. Her entire life will be story problems.

I feel bad for those who don't see it. It isn't about knowing the math, it is about understanding what is going on around you. And why.

[Love Life]

Funny story on math use.

Myself and few buddies were laughing it up in boot camp about how all the stupid stuff (mainly math) we learned in high school was a waste of time now that we were becoming meat eaters.

Fast forward to SOI and one of those buddies became a mortarman!! Hahaha!! Then another of those buddies in that group became a scout sniper. Hahahaha again!!!

[btroj]

Hmmmm, a bit of math for them? Maybe some vectors and trig too?

[Love Life]

Something along those lines. Suckers...

[DRNurse1]

Funny story on math use.

Myself and few buddies were laughing it up in boot camp about how all the stupid stuff (mainly math) we learned in high school was a waste of time now that we were becoming meat eaters.

Fast forward to SOI and one of those buddies became a mortarman!! Hahaha!! Then another of those buddies in that group became a scout sniper. Hahahaha again!!!

Love Life: were you able to rise out of the dirt like your buddies??? Survival of the fittest, right?

[Love Life]

If your question is: Have I remained competitive and gotten promoted? Then yes. I have promoted faster than them and have survived.

Next question please.

[btroj]

Survived is always a good start point.

Isn't it amazing how stuff you don't think will ever have use can come back to bite you? How many guys realize that artillery, mortars, snipers, and who knows who else use math!

Maybe boot camp should teach calculus!

[frkelly74]

So life is a story problem. I like that and will use it, thank you.

[felix]

Sooner or later, promotion will be based upon the ability (math or personality) to handle money or the means to make/save the same for the "system". Why? Because they say so! ... felix

[Love Life]

Isn't it amazing how stuff you don't think will ever have use can come back to bite you? How many guys realize that artillery, mortars, snipers, and who knows who else use math!


We have all found it funny. However; for all the math gurus here, I'd like you to sit down and write out a 5 paragrapgh order. That will make you want to take your pencil to your eyes.

[btroj]

I could write it but you wouldn't be able to read it. I have developed a bad case of Dr penmanship.......

[pipehand]

Love Life, the last time I had to write out a 5 paragraph order was 1986. Check if I remember right:

Situation

Mission

Enemy

Admin & Logistics

Communication


Trig I use bunches on the job, both in determining odd angle takeouts for pipe fittings and also for location/coordinates of runs that don't go north/south or east/west. Algebra, not so much.

Like MtGun44, I've also taught math to adults. It's a big difference teaching someone that has a use for the math versus a kid in school that has no framework to understand how the math can be used as a tool. Word problems help, and also help the student separate significant info from useless info. For instance:

"You're driving down the road in your canoe at 45 miles an hour when one of the wheels falls off. How many pancakes does it take to shingle a doghouse?"

[Tom Myers]

.....2
12y -5y -2 = 0

We home school and our middle daughter has run into an equation that we can't solve to match the answer in the book.

it should read 12y squared - 5y -2 =0

I know there are some who understand the correct way to factor this out and might offer us some instruction on this.

thank you

Perhaps the instructor is expecting your daughter to make use of the standard quadratic equation to solve this type of equation.

ax² + bx + c = y

The equation can be solved for x with the quadratic formula which give two answers for x.

x = (-b ± SqRoot[ b² - 4*a*c ] ) / 2 / a

which states that x equals minus b, plus or minus the square root of b squared minus 4 times a times c. then divide all that by two and then by a.

This will usually give on positive answer and one negative answer.

In your daughter's problem we can first write the equation as

12x² - 5x - 2 = 0

Then substituting the values into the quadratic equation, and paying attention to the plus and minus signs, we get

x = (- [-5] ± SqRt[ (-5)² - 4 * 12 * -2 ] ) / 2 / 12

Doing the math inside the brackets we get

x = ( 5 ± SqRt[ 25 + 96] ) / 2 / 12 or

x = ( 5 ± SqRt[ 121 ] ) / 24 Then

x = ( 5 + 11 ) / 24 = 0.666667 or

x = ( 5 - 11 ) / 24 = -0.25

So substituting x back to y in your daughter's equation

The equation has two answers + 0.666667 and -0.25

Or more simply 2/3 and -1/4

[MT Gianni]

Survived is always a good start point.

Isn't it amazing how stuff you don't think will ever have use can come back to bite you? How many guys realize that artillery, mortars, snipers, and who knows who else use math!

Maybe boot camp should teach calculus!

In "The Third Bullet" Stephen Hunter says that ballistic tables and equations and a large infatuation with them, predate in door plumbing and flush toilets. Share that with your liberal friends.

[RED333]

Stop, yall are making my head hurt.
Found with Google
Are you trying to solve for y?

12y-5y-2=0
12y-5y=0+2
7y=2
y= 2/7

[frkelly74]

.666667 is 2/3 I think.

[45 2.1]

.666667 is 2/3 I think.

Close enough, as it is rounded to a certain significant figure.... 2/3 is actually an irrational number, usually written as 0.666 with a horizontal bar above the last number which means that number repeats and goes on FOREVER............

[GL49]

(-1/4)squared = 1/16. So…..

12(1/16) -5(-1/4) -2 = 0

12/16 +5/4 -2 = 0

3/4 +5/4 -2 = 0

Seems to work for me.

Where am I going wrong?

[45 2.1]

You haven't.... getting old s()ks..... can't read my own scribbling and missed a sign change. Not very often you see two answers for one variable though.

[GL49]

You haven't.... getting old s()ks..... can't read my own scribbling and missed a sign change. Not very often you see two answers for one variable though.

Yes, it does. Been there, am that.

(I will admit that before I posted I had my college-age son who's majoring in math double check my work.)

[fouronesix]

Stop, yall are making my head hurt.
Found with Google
Are you trying to solve for y?

12y-5y-2=0
12y-5y=0+2
7y=2
y= 2/7

Ya, that was the "simple" algebraic equation. But the real equation turned out to be and was added in the OP as a standard trinomial: 12y squared - 5y - 2 = 0.

An academic exercise for the home school math problem but in practical application looks like a two point, curvilinear intersect of the y axis. With the solution being y = (-.25, .66__)

My head hurts too, been sooooo long since having to do that sort of stuff :)
Taking two aspirin and gong to bed.

[theperfessor]

I thought the rule was that you could (but didn't necessarily always have) at least one zero solution for each power of the variable in the equation, i.e. An equation of the form ax+b=0 could have one zero solution for x, an equation such as ax^2+bx+c=0 could have two zero solutions for x, and so forth.

Hope I haven't misunderstood the discussion here.

[GL49]

I thought the rule was that you could (but didn't necessarily always have) at least one zero solution for each power of the variable in the equation, i.e. An equation of the form ax+b=0 could have one zero solution for x, an equation such as ax^2+bx+c=0 could have two zero solutions for x, and so forth.

Hope I haven't misunderstood the discussion here.

Thats kind of what I remember, but once I got to Calculus, Differential Equations, etc. in college, that kind of information just got squeezed out of my head through my ears.

[45 2.1]

Thats kind of what I remember, but once I got to Calculus, Differential Equations, etc. in college, that kind of information just got squeezed out of my head through my ears.

Spatial applications in surveying and design when we didn't have ANY computers works harder on you. (X,Y,Z) coordinates are fun that way.

[Tom Myers]

.666667 is 2/3 I think.

Yep, you'r right. I went back and corrected it. Typos can really make me look stupid sometimes.

[IllinoisCoyoteHunter]

E=mc^2

[felix]

Tom Myers has the problem correctly stated by introducing the second variable. ... felix