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Finding the root of a function? watch

1. e.g. for 2x - 3y = 6

I think I can do this to find the root (putting 0 in for y)

2x - 3y = 6
2x - 3(0) = 6
2x = 6
x = 3

But when you have one more term e.g. 4x+3y+12=0 could you still use the same "method"?

4x + 3y(0) + 12 = 0
4x + 12 = 0
12/-4x = -3 (or something? )
2. (Original post by tymbnuip)
e.g. for 2x - 3y = 6

I think I can do this to find the root (putting 0 in for y)

2x - 3y = 6
2x - 3(0) = 6
2x = 6
x = 3

But when you have one more term e.g. 4x+3y+12=0 could you still use the same "method"?

4x + 3y(0) + 12 = 0
4x + 12 = 0
12/-4x = -3 (or something? )

they're the same type of question

2x - 3x = 6 can be written as 2x - 3x - 6 = 0,

just as 2x + 3y + 12 = 0 can be written as 2x + 3y = -12.
3. yes you can!

4x + 3y(0) + 12 = 0
4x + 12 = 0
x = -3

however, do remember that these equations have infinitely many solutions.

for eg, x = 0, y = -4 is also a solution to the second problem. if you plot these points on a graph, you will get a straight line.
4. So can I then find a "slope"?
5. rewrite the equation in the form:
y = mx+c,
then, slope = m
6. 4x + 3y + 12 =0
3y= -4x - 12
y= -4/3x - 4

Then you get the 'slope', which is -4/3
(Haven't done any maths during summer so hope my answer is right lol )
yes you can!

4x + 3y(0) + 12 = 0
4x + 12 = 0
x = -3

however, do remember that these equations have infinitely many solutions.

for eg, x = 0, y = -4 is also a solution to the second problem. if you plot these points on a graph, you will get a straight line.
I think, given they're asking for a "root" they mean solutions (x,0) rather than general solutions (x,y), i.e. they're interested in where this line crosses the x-axis
8. (Original post by RichE)
I think, given they're asking for a "root" they mean solutions (x,0) rather than general solutions (x,y), i.e. they're interested in where this line crosses the x-axis
Yep I agree
9. So is the root still (-3,0) for 4x+3y+12=0?
10. 1 1111
11. (Original post by tymbnuip)
So is the root still (-3,0) for 4x+3y+12=0?
Yep. You'd probably just call the root "3" or "x = 3" though, as a root is always when y = 0.
12. (Original post by RichE)
I think, given they're asking for a "root" they mean solutions (x,0) rather than general solutions (x,y), i.e. they're interested in where this line crosses the x-axis
Root of an equation - (Alg.) that value which, substituted for the unknown quantity in an equation, satisfies the equation. (http://www.thefreedictionary.com/Root+of+an+equation)

thereafter, the equation 4x + 12 = 0 has only one solution whereas
the equation 4x + 3y + 12 = 0 has infinitely many solutions.
13. So for 2x-3y=6 (to find the slope) I would rewrite as 2x-3y-6=0.

Then rewrite in form y = mx+c.

2x - 3y - 6 = 0
3y= -2x - 6
y= -2/3x - 2 = -2/3 for slope? Though the answer doesn't have a minus in apparently - why has mine got a negative in? (n00b question)
thereafter, the equation 4x + 12 = 0 has only one solution whereas
the equation 4x + 3y + 12 = 0 has infinitely many solutions.
I think the implication is that a "root" is when y = 0, so although 4x + 3y + 12 = 0 has infinitely many solutions (x, y), it has only one root (-3).
15. (Original post by tymbnuip)
3y= -2x - 6
incorrect.

3y= 2x - 6
m=2/3
16. (Original post by tymbnuip)
So for 2x-3y=6 (to find the slope) I would rewrite as 2x-3y-6=0.

Then rewrite in form y = mx+c.

2x - 3y - 6 = 0
3y= -2x - 6
y= -2/3x - 2 = -2/3 for slope? Though the answer doesn't have a minus in apparently - why has mine got a negative in? (n00b question)
You've made a sign error in moving to the bit I've put in bold. The method is correct, however.

Also, the equals sign I've put in red isn't correctly used. y doesn't equal -2/3 (which your equals sign implies), the slope does. You could've written "therefore" where the equals sign is. It's a bad habit to get into, as it looks bad, it's incorrect and you'll get marked down in exams for it.
17. (Original post by tommm)
I think the implication is that a "root" is when y = 0, so although 4x + 3y + 12 = 0 has infinitely many solutions (x, y), it has only one root (-3).
We usually talk about roots in equations of one variable. For example, x = 0 and x = 5 are roots of the equation x2 -5x = 0

when there are multiple variables, and too few equations there are infinitely many solutions.
18. (Original post by Green Clover)
4x + 3y + 12 =0
3y= -4x - 12
Are the signs right in this ? i.e. should it be

3y = 4x +12
19. Anyone?
20. What Green Clover put is correct.

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