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Thread: can't for the life of me undestand this

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    Future USMC Cobra Pilot Member Prussian to the Iron's Avatar
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    Default can't for the life of me undestand this

    okay, so ive been doing better with my algebra II, but i am still having tons of trouble. these questions in particular i have no idea about. the book/commentary didnt even explain double roots, and i can't call the teacher for help with a test. any help?

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    Prince of Maldonia Member Toby and Kiki Champion, Goo Slasher Champion, Frogger Champion woad&fangs's Avatar
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    Default Re: can't for the life of me undestand this

    According to my memory and this page

    A double root is when the parabola just touches the x axis instead of crossing it. If the equation were to cross the x axis at -6 and 5 then those would be your answers. If the equation touches the x axis at 3 but doesn't cross it then the answer would be double root at 3.

    Hopefully that helps
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    Future USMC Cobra Pilot Member Prussian to the Iron's Avatar
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    Default Re: can't for the life of me undestand this

    .......................sorry my brain just broke for a couple minutes.........

    uuuuuhhhhhhhhhhh............................what?
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    master of the pwniverse Member Fragony's Avatar
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    Default Re: can't for the life of me undestand this

    double root is omega

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    Default Re: can't for the life of me undestand this

    riiiiiiiiiiiightttt.................................................???????
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    Host Member Maeda Path Champion, Arkanoid Champion, 3D SuperBall Champion, Simon Champion, Disc Dash Champion, Breakout Champion Zain's Avatar
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    Default Re: can't for the life of me undestand this

    If you were to graph the equations, typically roots are the part where the parabola (curvy line) crosses the x-axis (horizontal straight line) a double root simply means that it is the only place where the curvy line (parabola) touches the horizontal straight line (x-axis).

    It's called a double root because usually there are two roots. But because there is one, it's double. Just to keep all the math stuff uniform.

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    Hǫrðar Member Viking's Avatar
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    Default Re: can't for the life of me undestand this

    How do you extract the roots? The "abc formula"? Whenever b^2-4ac = 0, you've got a double root, where the quadratic equation is on the form ax^2 + bx + c.

    E.g. x^2 + 2x + 1 gives the double root -1.

    My calculus books calls them single roots; though since I am no mathematician I shan't enter an argument..
    Last edited by Viking; 10-27-2009 at 22:24.
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    Master of useless knowledge Senior Member Kitten Shooting Champion, Eskiv Champion Ironside's Avatar
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    Default Re: can't for the life of me undestand this

    Basically all x^a functions have a roots. If you have less solutions than roots, then some roots are double or larger roots.

    x^87=0 have 87 roots but 1 solution (namely 0), so that's one 87 root. Understand the concept, not my words (as they're probably described differently in the books).

    They appear when a term is repeated (x+4)^3*(x-3)=0 have 4 roots and 2 solutions (-4, 3). Because the first term is repeated three times, -4 becomes a trippel root.
    (aka full answer is -4, -4, -4, 3)

    As I take it this is part of a test, I'll refrain from giving the correct answers.
    We are all aware that the senses can be deceived, the eyes fooled. But how can we be sure our senses are not being deceived at any particular time, or even all the time? Might I just be a brain in a tank somewhere, tricked all my life into believing in the events of this world by some insane computer? And does my life gain or lose meaning based on my reaction to such solipsism?

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    Future USMC Cobra Pilot Member Prussian to the Iron's Avatar
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    Default Re: can't for the life of me undestand this

    okay, guys, try to explain this like you're explaining it to a 10 year old. i simply have no idea even when you are trying to help. the book makes no sense of it either.
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    Host Member Maeda Path Champion, Arkanoid Champion, 3D SuperBall Champion, Simon Champion, Disc Dash Champion, Breakout Champion Zain's Avatar
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    Default Re: can't for the life of me undestand this

    Quote Originally Posted by Prussian Iron View Post
    okay, guys, try to explain this like you're explaining it to a 10 year old. i simply have no idea even when you are trying to help. the book makes no sense of it either.
    I put it as simply as I could dude...

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    Hǫrðar Member Viking's Avatar
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    Default Re: can't for the life of me undestand this

    Quote Originally Posted by Prussian Iron View Post
    okay, guys, try to explain this like you're explaining it to a 10 year old. i simply have no idea even when you are trying to help. the book makes no sense of it either.
    What method do you use to find the roots? Don't you have any?
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    Future USMC Cobra Pilot Member Prussian to the Iron's Avatar
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    Default Re: can't for the life of me undestand this

    i dont even know what a root is. it doesnt even say, it just tell us to find the roots, gives us an example, than leaves us to screw ourselves over.
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    Host Member Maeda Path Champion, Arkanoid Champion, 3D SuperBall Champion, Simon Champion, Disc Dash Champion, Breakout Champion Zain's Avatar
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    Default Re: can't for the life of me undestand this

    Quote Originally Posted by Prussian Iron View Post
    i dont even know what a root is. it doesnt even say, it just tell us to find the roots, gives us an example, than leaves us to screw ourselves over.
    Roots are where the line crosses the x-axis.

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    Future USMC Cobra Pilot Member Prussian to the Iron's Avatar
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    Default Re: can't for the life of me undestand this

    okay. now how fo i find the roots?
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    Parthian Cataphract #03452 Member Zradha Pahlavan's Avatar
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    Default Re: can't for the life of me undestand this

    Algebra 2 makes my brain hurt, but I'll see if I can help.

    This is a parabola:


    Where the curvy line crosses or touches the straight horizontal line (it can be anywhere on that line) is where the root is. I think.
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    Host Member Maeda Path Champion, Arkanoid Champion, 3D SuperBall Champion, Simon Champion, Disc Dash Champion, Breakout Champion Zain's Avatar
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    Default Re: can't for the life of me undestand this

    Quote Originally Posted by Zradha Pahlavan View Post
    Algebra 2 makes my brain hurt, but I'll see if I can help.

    This is a parabola:


    Where the curvy line crosses or touches the straight horizontal line (it can be anywhere on that line) is where the root is. I think.
    In this example, the root is 0 because that is where the red line (parabola) crosses the horizontal x-axis.

    Understand now?

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    Master of useless knowledge Senior Member Kitten Shooting Champion, Eskiv Champion Ironside's Avatar
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    Default Re: can't for the life of me undestand this

    Quote Originally Posted by Prussian Iron View Post
    i dont even know what a root is. it doesnt even say, it just tell us to find the roots, gives us an example, than leaves us to screw ourselves over.
    Roots are the value where the equation can be solved and the answer is 0.

    Take (x-2)^2=0 for example, the roots are then (2, 2) a double root. (x-2)^2=16 on the other hand have the solutions (6,-2) as you can see if you put those values in.

    Now by a general rule, the prefered method is to write it in this form f(x)=y where y=0, so (x-2)^2=16 becomes (x-2)^2-16=0. It has the same solutions, but it is in this form the roots are where the curve touches or crosses zero. So the roots are (6,-2) same as above, so you don't have to make the equation in the f(x)=0 form to solve it, but you'll need to understand the concept.

    Viking has given one formula to calculate the roots, but these are easy enough to solve by asking yourself "what values of x make this equation 0?" (that is f(x)=0). The double roots are already explained properly I think.

    Can't explain properly why this is done, but it has to do with making more advanced math easier. For you, it would melt your brain atm.
    We are all aware that the senses can be deceived, the eyes fooled. But how can we be sure our senses are not being deceived at any particular time, or even all the time? Might I just be a brain in a tank somewhere, tricked all my life into believing in the events of this world by some insane computer? And does my life gain or lose meaning based on my reaction to such solipsism?

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    Future USMC Cobra Pilot Member Prussian to the Iron's Avatar
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    Default Re: can't for the life of me undestand this

    so how would i be able to see how i should graph the parabola so i can see the answer?
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    Master of useless knowledge Senior Member Kitten Shooting Champion, Eskiv Champion Ironside's Avatar
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    Default Re: can't for the life of me undestand this

    Quote Originally Posted by Prussian Iron View Post
    so how would i be able to see how i should graph the parabola so i can see the answer?
    Graphs are only really useful if you got a graph drawing calculator. You normally solve them the same way you solve normal equations, with the exception of that they have multiple answers or a single answer with a double root (if it's a x^2 function that is). All examples given are possible to solve by head counting, even if 11 is severely helped by the possible answers.

    It will get slightly more complicated soon I suspect, but it is a speciffic formula for those functions.

    Anyway, the more literal answer on your question (drawing a graph by hand) would be to put in some x values in the function, get the y values and then plot them together in a x/y system.
    We are all aware that the senses can be deceived, the eyes fooled. But how can we be sure our senses are not being deceived at any particular time, or even all the time? Might I just be a brain in a tank somewhere, tricked all my life into believing in the events of this world by some insane computer? And does my life gain or lose meaning based on my reaction to such solipsism?

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    Future USMC Cobra Pilot Member Prussian to the Iron's Avatar
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    Default Re: can't for the life of me undestand this

    I have a graphing calculator, but it only uses Y= when graphing. how can i get to it? could you walk me through one of the questions so i can check if I'm doing it right?
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    Default Re: can't for the life of me undestand this

    I don't really understand ‘double roots’ as proper terminology either; but if you need to mark the points in which a function f touches upon a certain line this is done not by solving for roots, but by finding the derivative function f' and then solving for f' = g' and f = g; where g' is the derivative of a function g describing said line. E.g. f(x) = x^2; g(x) = 0 => f'(x) = 2x; g' = 0 => f' = g' and f = g if and only if x = 0.

    That test is fairly trivial to answer: since it's multiple choice, plug in one of the values see if it works out. E.g.: x^4 = 36x^2 => 36 = x^2 => set of solutions for x = {-6, 6}. Or: x^4 = 36x^2 = 0 => x = 0. So: solutions for x = {-6, 0, 6}. But you could get that easily via process of elimination and a careful review of your answer; at least if you are good at calculation inside your head this'll be faaar faster than properly deriving answers to questions you struggle to understand.

    For bonus points:
    Compared to the abc formula; for a formula of ax^2 + bx + c; with a, b and c not 0: factorization into forms such as (dx + e)(fx + g) is a more efficient approach to deriving solutions for equations since you want to solve for x that evaluates to 0, and multiplication like this gives you a trivial & painless way to evaluate just that.
    @Ironside: (x-2)^2 = 0 => (x-2) = sqrt(0) => (x-2) = 0 => x = 2.
    Last edited by Tellos Athenaios; 10-29-2009 at 19:00.
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    Deadhead Member Owen Glyndwr's Avatar
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    Default Re: can't for the life of me undestand this

    This kind of stuff is why I'm really glad I tested out of math and don't have to take any math classes in University!!

    Good luck my friend.
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    Master of useless knowledge Senior Member Kitten Shooting Champion, Eskiv Champion Ironside's Avatar
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    Default Re: can't for the life of me undestand this

    Quote Originally Posted by Tellos Athenaios View Post
    @Ironside: (x-2)^2 = 0 => (x-2) = sqrt(0) => (x-2) = 0 => x = 2.
    I think I got a nice way to explain a double root here.

    (x-2)^2=(x-2)(x-2)=0 . Gives one 2 for the first paranthesis (root 1) and a second 2 for the second (root 2) paranthesis. They just happen to be the same number.

    Compare to (x-1)(x-3)=0 => (1 (root 1), 3 (root 2))

    Same principles, just a special case. Same as elips => circle, rectangle => square etc. Not that much simplification bonus in this case though.

    Quote Originally Posted by Owen Glyndwr View Post
    This kind of stuff is why I'm really glad I tested out of math and don't have to take any math classes in University!!

    Good luck my friend.
    You mean you don't like to do iterations by hand to solve partial differential equations?

    Spoiler Alert, click show to read: 
    Those are mean, but computers loves them. Until you make them complicated enough to cause work overload...
    We are all aware that the senses can be deceived, the eyes fooled. But how can we be sure our senses are not being deceived at any particular time, or even all the time? Might I just be a brain in a tank somewhere, tricked all my life into believing in the events of this world by some insane computer? And does my life gain or lose meaning based on my reaction to such solipsism?

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    Hǫrðar Member Viking's Avatar
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    Default Re: can't for the life of me undestand this

    Quote Originally Posted by Ironside View Post
    You mean you don't like to do iterations by hand to solve partial differential equations?

    Spoiler Alert, click show to read: 
    Those are mean, but computers loves them. Until you make them complicated enough to cause work overload...
    What...do you mean that you had to solve those equations numerically by hand?
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    Future USMC Cobra Pilot Member Prussian to the Iron's Avatar
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    Default Re: can't for the life of me undestand this

    Quote Originally Posted by Ironside View Post
    I think I got a nice way to explain a double root here.

    (x-2)^2=(x-2)(x-2)=0 . Gives one 2 for the first paranthesis (root 1) and a second 2 for the second (root 2) paranthesis. They just happen to be the same number.

    Compare to (x-1)(x-3)=0 => (1 (root 1), 3 (root 2))
    so in that example the double root would be....

    1,???
    and
    3,???

    correct?
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    Hǫrðar Member Viking's Avatar
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    Default Re: can't for the life of me undestand this

    Quote Originally Posted by Prussian Iron View Post
    so in that example the double root would be....

    1,???
    and
    3,???

    correct?
    A double root is a root that occurs twice. In the first example, the root '2' occurs twice. In the second, no root occurs twice.

    A root is the x value for which the function is zero, which is also a place where it crosses the x-axis. So, if you plot the funtcion y = (x-2)(x-3), the function will cross the x-axis at x = 2 and x = 3, because

    y(2) = (2-2)*(2-3)
    = 0*(-1)
    = 0

    Same goes for x = 3.

    What you should do, though, is apparently to plot the function and find out where it crosses the x-axis.

    Let's say you want to find the roots for

    x^2 + 3x = - 2

    you have to rearrange the equation such that the right hand side of it equals zero. This can be done by adding 2 on both sides:

    x^2 + 3x + 2 = - 2 + 2
    x^2 + 3x + 2 = 0

    now you plot y = x^2 + 3x + 2, because this is the function you want to equal zero.

    Alternatively, you may plot y = x^2 + 3x and find out where this equals -2.
    Last edited by Viking; 10-30-2009 at 18:32.
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    Future USMC Cobra Pilot Member Prussian to the Iron's Avatar
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    Default Re: can't for the life of me undestand this

    so would number 10 be C? or A? I'm guessing A right?
    Last edited by Prussian to the Iron; 10-30-2009 at 18:32.
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    Hǫrðar Member Viking's Avatar
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    Default Re: can't for the life of me undestand this

    Try to insert e.g. x = 3 in the equation and see what you get. Remember that you are looking for the solutions of an equation.
    Last edited by Viking; 10-30-2009 at 19:09.
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    Future USMC Cobra Pilot Member Prussian to the Iron's Avatar
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    Default Re: can't for the life of me undestand this

    so C then!
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    Hǫrðar Member Viking's Avatar
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    Default Re: can't for the life of me undestand this

    Does the left hand side of the equation equal the right hand side if x is the number three?


    If you have the equation

    (x-2)(x-1) = 2

    and set x = 2

    you get...

    (2-2)(2-1) = 2

    0*(2-1) = 2

    0 = 2

    which is impossible. Hence x = 2 cannot be a root.

    I think you should rearrange the equation and plot it, as I suggested; otherwise you are meant to do it otherwise. How does the example in the book find the root(s)?
    Last edited by Viking; 10-30-2009 at 19:30.
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