Question

if (x+2)(x-6)=0 then we say either x+4=0 or x-6=0
why not we say x+4=0 and x-6=0?

Answer 1

Well x is either -4 or it's 6, it can't be both...

Answer 2

That's... yeah... pretty much the sum of it. x can only have a distinct value.

Answer 3

if (x+2)(x-6)=0 then we can not say either x+4=0 or x-6=0

Answer 4

pretend that x is like time. It is either 4 minutes ago or 6 minutes in the future, it cannot be both at the same time not even in

Back to the Future

Answer 5

Ha! FFM! We can say that x+2 = 0 or x-6 = 0 :-P

Answer 6

Yep!

Answer 7

ok when we have xy=0 then why we say either x=0 or y=0 why not we say x=0 and y=0

Answer 8

Hahaha you were the only one to notice.

Answer 9

It's an inclusive "or".

Answer 10

If it's xy = 0 then x and y COULD both be 0, or one could be 0.

Answer 11

its either

Answer 12

You can't work anything out from xy = 0. If you're given that as an equation, the absolute best you can calculate is that either one or both x and y are equal to 0. Beyond that only speculation is possible, as if one variable is 0 the product is 0 and the other could therefore be anything.

Answer 13

(I mean literally xy = 0. Obviously you can work out {equation containing x and y} = 0).

Answer 14

if (x+4)(x-6)=0 then we say either x+4=0 or x-6=0

The constraint "or" is to avoid division by zero.

Answer 15

are all of u sure that if xy=0 then both x and y can be zero. 100% sure?

Answer 16

It is like saying I will go get groceries on Tuesday or Wednesday, you need to do it one of the days, but you may go both days as well.

Answer 17

Yes :)

Answer 18

They can both be zero, absolutely, but they do not have to both be zero and in most math problems the are not both zero.

Answer 19

\( xy=0 \) If both are zero, then \( x = \frac{0}{y} \) but y is zero too, Disaster !!!

Answer 20

FFM I dunno if this is the thread to bring that up :)

Answer 21

have any of u read vector space. in which i have read if v is a vector and k is a constant/scalar then if kv=0 and v=0 then v is linearly dependent bcz k would be non zero.

Answer 22

That is not correct, regarding vector spaces.

Answer 23

But if we have xy = 0, we cannot assume x = 0/y is a viable option. If we have xy = 0, then they both may be zero.

Answer 24

>"But if we have xy = 0, we cannot assume x = 0/y is a viable option"

why ? That's an equation, division by \( y \) on both sides is perfectly valid.

Answer 25

No it's not. Division by zero is never valid.

Answer 26

Yes that's why we can't have both zero.

Answer 27

who is to say that y is a function of x?

Answer 28

what is the logic of ur answer. anything is correct for calculus is false for vector spaces.

Answer 29

That's why the "or"

Answer 30

That's not true at all.

Answer 31

i define x=0 and y=0 then xy=0.....both zero

Answer 32

You may only divide if you make the assumption that y is not zero.

Answer 33

lol, Zarkon that's alright then, I assumed y is the dependent variable ;)

Answer 34

I don't understand what that has to do with anything... two quantities multiplied together equals zero. Either the first is zero, the second is zero, or both are.

Answer 35

It depends on the definition on X = (x+4) and Y=(x-4), and (x+4)(x-4)=0 then we can't have both zero, as they have same independent variable

Answer 36

in order for ab = 0, only one value needs to be zero. They can't both be zero because a doesn't equal b. They have to be two different numbers.

Answer 37

Just because we have multiplication, it does not mean that we can divide. This is the reason we get extraneous solutions in algebra.
If we have

a = 5

and

x(a - 5) = 0

we cannot divide both sides by a-5.

Answer 38

but if x and y are not defined then?

Answer 39

what do you mean be not defined ? They have to defined.

Answer 40

Obviously if y = (x+2) both can't be zero but we resolved that question like four posts in. In general, xy = 0 implies x = 0, y = 0, or both x and y = 0.

Answer 41

In general, xy = 0 implies x = 0, y = 0, or both x and y = 0. -- No, the both part depends on the definition of x and y.

Answer 42

ab = 144 implies that a and b are different?

Abe is 12 and Barney is 12, they are twin brothers, who happen to be 12, they cannot be the same age?

Answer 43

as for your vector space question...are you asking if the the set consisting of only the zero vector linearly dependent?

Answer 44

In general. In general. In general.

Answer 45

If they are not defined, then they are unknown and they may BOTH be zero

Answer 46

In general I always assume y is a function of x ;)

Answer 47

a = 3 b = 0

3*0 = 0

a = 0, b = 4

0*4 = 0

When dealing with factorable quadratics, a and b will never both be zero.

Answer 48

haha FFM have you never worked with two variables, then? And Hero, yeah, but that's not what I am talking about.

Answer 49

yes zarkon i want to ask the same

Answer 50

(0)(0)=0

Answer 51

For

a^2 - b^2 = 0

One solution is a = 4 and b = 4

Answer 52

JeMurray, I was only talking to Rosy, not you.

Answer 53

the set \[S=\{\vec{0}\}\] is a linearly dependent set

Answer 54

Duly noted Hero, sorry :)

Answer 55

they can be both equal to 0

Answer 56

how it is linearly dependent zarkon?

Answer 57

it is dependent because you can write a linear combination equal to zero in a nontrivial way

Answer 58

@zarkon that's what i want to ask if we write it in non-trivial way then it means scalar is non zero i.e if kv=0 and v=0 then k must be non zero. means in kv=0 k and v both can't be both zero but in xy=0 all of you have said that both can be zero what is this??????????????????????
please answer me soon.........

Answer 59

Let me clarify what I think you mean when you talk about vector spaces.
Let V be a vector space containing three vectors,
\[ V = \{\vec{v}_1, \vec{v}_2, \vec{v}_3 \}\]
The vectors
\[\vec{v}_1,\vec{v}_2,\text{ and } \vec{v}_3\]
are linearly dependent if you can write
\[a\cdot \vec{v}_1 + b\cdot \vec{v_2} + c\cdot \vec{v_3} = \vec{0}\]
where a, b, and c are not all zero.
Zarkon said that the collection
\[V = \{\vec{0}\} \]
is linearly dependent. This is of course true, because
\[ a \cdot \vec{0} = \vec{0} \]
for any constant number a.

Answer 60

yes but it can be linearly dependent when a is not equal to zero and question still remain the same why it can not be zero why?????????????

Answer 61

There is no mathematical reason that a could not be zero. We simply don't allow a to be zero when we're talking about linear dependence.

Answer 62

a=0 works (\(0\vec{0}=\vec{0}\)), but so does a=5 or a=-7

all the definition says (for linear dependent) is that there is a way to write the linear combination so that not all the coefficients are zero, but the L.C. is the zero vector

Answer 63

i think you do not understand my que. i am just asking that in linear dependence we say if v=0 then kv=0 is linear dependent bcz k is non zero on the other hand in xy=0 we say both x and y can be zero. isn't it strange???

Answer 64

S={v} , (v=\(\vec{0}\)) is linearly dependent because it is possible to write kv=\(\vec{0}\) where k is not zero. you could also let k=0 then it is still true that kv=\(\vec{0}\)