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10 replies to this topic

#1 jon2005

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Posted 04 December 2005 - 01:45 AM

A part of a circuit is represented by a curve with the equation y=5-2x^2-x^3 and the proposed sliproad is given by straight line with equation y= -4x-3.

The two lines meet at B, find algebraically the coordinates of B.

This question is bugging me, I know you put them equal to each other but I cant work out what you do next :S

thanks in advance.

#2 Steve

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Posted 04 December 2005 - 12:16 PM

Yeah, you are right.

The x-coordinate of the point of intersection is the solution to the equation:



\begin{align*}
5 - 2x^2 - x^3 &= -4x-3 \\
x^3 + 2x^2 - 4x -8 &= 0
\end{align*}

Then you can factorise this using synthetic division. (If you haven't covered that yet, then that'll be why you don't know how to do it!)
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#3 jon2005

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Posted 04 December 2005 - 03:21 PM

QUOTE(Steve @ Dec 4 2005, 12:16 PM)
Yeah, you are right.

The x-coordinate of the point of intersection is the solution to the equation:



\begin{align*}
5 - 2x^2 - x^3 &= -4x-3 \\
x^3 + 2x^2 - 4x -8 &= 0
\end{align*}

Then you can factorise this using synthetic division. (If you haven't covered that yet, then that'll be why you don't know how to do it!)

View Post



Cheers,
I ended up with x= -2 and y=5.

Just wondering, is there a rule of thumb for when to use synthetic division, and when do you complete the square?

thanks

jon.

#4 Steve

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Posted 04 December 2005 - 04:01 PM

Comleting the Square is really for working with quadratics.

If you want to solve a quadratic, I suppose you could complete the square, but you can also just factorise normally (or use synthetic division if you find this difficult).

PS You should get more that one value of x from solving the equation in the question.
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#5 jon2005

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Posted 04 December 2005 - 05:31 PM

Thanks for clearing that up,

yeah I ended up with more than one value but the other one was in the positive axis of x and as the point where they meet is clearey where x<0 I disregarded it.

ta,

jon.

#6 x_Claire_x

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Posted 18 May 2006 - 10:28 AM

why don't i know what synthetic division is crying.gif ohmy.gif
what is it? sad.gif
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#7 Gray

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Posted 18 May 2006 - 10:33 AM

The thing that you use to find a factor of a polynomial. It's pretty easy.

See: http://www.hsn.uk.net/files/HSN22100.pdf
It's topic 9.

Hope that helps. smile.gif

#8 x_Claire_x

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Posted 18 May 2006 - 11:12 AM

aww, we never told it was called that, was getting worried there lol!
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#9 Nathan

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Posted 18 May 2006 - 11:14 AM

nah us neither...the teacher jus called it "the big L" , i guess it stops you getting confused with useless information

#10 Joel

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Posted 18 May 2006 - 11:58 AM

QUOTE(nathanm @ May 18 2006, 12:14 PM) View Post
nah us neither...the teacher jus called it "the big L" , i guess it stops you getting confused with useless information
You're teacher really should have taught you the proper names for things. If you got a question in the exam saying "solve......using synthetic division" it certainly wouldn't be useless information knowing what it meant.

#11 George

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Posted 18 May 2006 - 01:05 PM

QUOTE(Joel @ May 18 2006, 12:58 PM) View Post

You're teacher really should have taught you the proper names for things. If you got a question in the exam saying "solve......using synthetic division" it certainly wouldn't be useless information knowing what it meant.

In this case, I don't think they would ever specify "synthetic division", since that's just one method for achieving the same result. In fact, I think some teachers don't even use synthetic division with their classes.





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