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1. Solve the equation: x4-8x2-9=0

2. Find all roots of the equation: 2X3-X2+10X-5=0

3. Two roots of a polynomial equation with real coefficients are 2+3i and √7.

a. Find two additional roots.

b. Find the degree of the polynomial.

My mind has gone blank

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My math is a bit rusty here, so I can't help you with 2 or 3, but with the first one, it's a play on the quadratic expression.  When you have an equation like ax^2 + bx + c = 0, x is going to be (-b +/- sqr(b^2-4ac))/2a.  In this case, however, the x we're trying to find is actually an  x^2.  So, for our equation:

a = 1

b = -8

c = -9

So, we come up with:

x^2 = (8 +/- sqr(-8^2 - 4*1*-9))/2*1

= (8 +/- sqr(64 + 36))/2*1

= (8 +/- sqr(100))/2

= (8 +/- 10)/2

= 18/2 or -2/2

= 9 or -1

So, to find x, instead of x^2, we'd take the square root of our two answers.  Since -1 has no square root, we're left with just 9 as a possibility, so, our final answer is 3.

I hope that helps.

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1. Solve the equation: x4-8x2-9=0

2. Find all roots of the equation: 2X3-X2+10X-5=0

3. Two roots of a polynomial equation with real coefficients are 2+3i and √7.

a. Find two additional roots.

b. Find the degree of the polynomial.

My mind has gone blank

:uglystupid2: :uglystupid2: :uglystupid2: :uglystupid2:  I have not a clue

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aside from the fact that you may never use that type of formula - let's think about what this teaches you. Problem solving, deciding the way to attack the problem, and the pure simple joy of being able to solve a difficult puzzle. I use that stuff everyday. :D

*hugs* it gets easier.

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Yeah, if all they had you do were too simple problems you would remember so much less.

Pretty much what water said.

http://www.math.hawaii.edu/~tom/maui.pdf

And several others. I thought the one above was best though.

http://scholar.google.com/scholar?q=use%20of%20algebra%20in%20the%20workforce&hl=en&lr=&oi=scholart

If you get any smarter water, I am going to have to try and marry you.   :wink:

Oh yeah, I want you for your body too water.  :smitten:

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Yeah, if all they had you do were too simple problems you would remember so much less.

Pretty much what water said.

http://www.math.hawaii.edu/~tom/maui.pdf

And several others. I thought the one above was best though.

http://scholar.google.com/scholar?q=use%20of%20algebra%20in%20the%20workforce&hl=en&lr=&oi=scholart

If you get any smarter water, I am going to have to try and marry you.   :wink:

Oh yeah, I want you for your body too water.  :smitten:

It's all yours doll ;)

:smitten:

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aside from the fact that you may never use that type of formula - let's think about what this teaches you. Problem solving, deciding the way to attack the problem, and the pure simple joy of being able to solve a difficult puzzle. I use that stuff everyday. :D

 

it teaches nothing - it is a total waste of time -  just a way for schools to make money

In fact it is worse then a total waste of time becuase the time could have been spent learning something that is really used in the real world.

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it does teach you things you might later need.

if you are in a position to quote prices and want to play with different discounts to reach a certain price then you will need to know the basics to get excel to do it right.

excel is powerful as a math tool, but only if you know some of the stuff yourself.

but enough geezing....

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it does teach you things you might later need.

if you are in a position to quote prices and want to play with different discounts to reach a certain price then you will need to know the basics to get excel to do it right.

excel is powerful as a math tool, but only if you know some of the stuff yourself.

but enough geezing....

I am very "with" resop on this.

I use excel everyday, and I use the problem solving skills I learned in school. All those math questions that were stories that you have to change into a formula?

Use it, everyday.

If a Ford plant in Canada needs 1080 luggage racks every day and the transit time is 10 hours, and they have 766 on hand, when do you need to ship more luggage racks? How many do you need to ship to cover the next trucks arrival? You have trucks every 6 hours. The last one left 2 hours ago.

1. They use roughly 45 racks per hour.

2. They are covered for 17 hours. With the intransit racks they are covered for 21 hours.

3. In 4 hours from now you need to ship 180 racks. (How do I know that - by inferring that they run 24 hours a day, with 6 truck windows, you have to be able to fit 180 pieces on a truck.)

Now, if the capacity of your line is 30 pieces per hour - you're fine, but if the tool breaks, or the cycle time drops to less than 30 pieces per hour, you're in trouble, Since you have to run 30 pieces per hour, (again by inference of 180 pieces per truck), for every 2 hours of downtime on your line you will drop the inventory at the customer by 1 1/2 hours.

Excel ain't gonna do that for you - it may do the math, but you still have to figure out how to make it work.

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Back to something I said in one of these once before.

You will use algebra EVERY day of your life practically. If you are any good at math at all.

How do you find out gas mileage. How do you know what size of an item to buy. How do you figure out Kbps. or kbs.(I guess I said that right.) Anyway if you are involved in computers (DUH)  :uglystupid2: Buy using 2 numbers and an equation to find the missing X. Actually you have been using algebra since the first grade or before as they are learning excelled today. You just did not know it. And they are just taking you to new levels of problem solving. So when someone tells me no you don't need it. I guess they must be very bad at Math.  :evil6:

You have also been in Geometry since a very early age also.How about the pegs in the holes with the little hammer. I did get the squre peg in the round hole once.  :evil6:

Just my thoughts.

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it teaches nothing - it is a total waste of time -  just a way for schools to make money

In fact it is worse then a total waste of time becuase the time could have been spent learning something that is really used in the real world.

I have to very strongly disagree on this one.  Over the past decade I've have a good variety of jobs, from making pizzas to supervising a parole call center to managing the inner workings of an internet service provider's network, and in every single case I've used algebra at the bare minimum, and in some cases strong calculus and applied it to my work.

A lot of times it comes into areas that you may not think of as algebra, but when you take the time to think them out, you'll realize that algebra is exactly what you're doing.  For example, say you were working at a pizza joint and a school called up to order 20 pizzas.  They order 6 sausage, 6 peperoni, and the rest they want to be extra cheese.  When you do the math to find out how many cheese pizzas they need, it comes out to 6 + 6 + x = 20.  As others have said, learning algebra in school helps you learn how to work through a problem like that.  Now, I'm sure that eventually you would find a way to figure out your answer without using algebra, but it would take you more time to do it, and when you're working at a fast paced job, the difference between 20 seconds to solve a problem and 5 minutes can mean the difference between having a job and not having a job.

If you move up the ladder a little higher to something like programming 3d video games, there is quite a bit more math involved than you might ever guess.  Pretend you're making a part in a video game where you need to draw a 3 dimensional bell in the game, and to determine how high it swings, you need to figure out the mass of it.  To do that, you'll need to find the volume of the bell, but since a bell is such an odd shape, you'll need to actually use calculus to graph the curve of your bell, then flip that curve around a 3 dimensional axis, then graph the inner curve and do the same and subtract them.  You might think that's an insane amount of work for a small bell that probably won't mean much to the game at all, but these days everything is about realism in games, and it's becoming harder and harder to get by with anything that doesn't make you wonder if you're looking through a window or looking at a computer screen.

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Good job Atnevon, and water said she had all the brains.  :wink2: (kidding) or was I?   :roll:

Don't forget point spreads on a game. Interest rate on buying home. How much to one odds in gambling. Carpenters building a house. How do you think it ends up square and plumb? Home appraisers. Roofing contractor. Everybody wondered how I could figure a roofs size and pitch so fast and ACCURATELY. Saved a lot of $$ on figuring properly. Even most insurance adjusters were not as good. They had to use pat short cut formulas.  :grin2:  BIG ONE at this time of year. Income tax preparation. Now how many things could you savemoney on daily if you could add without taking off your shoes, or using a calculator. People have actually called me a walking calculator.  :grin2: I just hate calculators if I don't need them. I mostly use it to make sure my bankbook comes out to the tee.( I find a need for no errors there. ) Or where their are lots of figures.

But we use it in a less literal way.

Maybe if you said it a little more directly, I could come up with a better answer for you.

Literal in what way??

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