# why are we interested in only those values of x for which y is zero?

#### PG1995

Joined Apr 15, 2011
832
Hi

I understand that when roots a quadratic equation is found, we are essentially finding values of x for which y or f(x) is zero. But what how does it help us? I mean why are we only interested in values of x which makes y zero. e.g. quadratic formula for finding roots could only be used for finding values of x for which y is zero but it won't help us if we want to know values of x for which y is 2. Will it? Likewise, while solving differential equations we are only interested in those values which make the differential function equal to zero. Regards
PG

#### steveb

Joined Jul 3, 2008
2,436
Hi

I understand that when roots a quadratic equation is found, we are essentially finding values of x for which y or f(x) is zero. But what how does it help us? I mean why are we only interested in values of x which makes y zero. e.g. quadratic formula for finding roots could only be used for finding values of x for which y is zero but it won't help us if we want to know values of x for which y is 2. Will it? Likewise, while solving differential equations we are only interested in those values which make the differential function equal to zero.

Regards
PG
The thing is, whenever you have a single variable equation that you need to solve, you can always rewrite it in the form f(x)=0.

Let's say you had a quadratic 6x^2+2x+5=2. You can simply move the 2 to the other side and get 6x^2+2x+3=0

Note that not all problems will result in a quadratic formula, but you can always get a form f(x)=0 to find x.

#### endlessness

Joined Apr 2, 2011
1
Hi

I understand that when roots a quadratic equation is found, we are essentially finding values of x for which y or f(x) is zero. But what how does it help us?

Regards
PG
Because any single-variable equation can be written as f(x)=0; then one can use root-finding algorithms to find a solution if it is not viable to find those numerically.

#### justtrying

Joined Mar 9, 2011
439
you use it to solve for all sorts of things...

#### BillO

Joined Nov 24, 2008
999
Mathematically it's quite arbitrary. The answers here are all correct, but it could be anything. Y=2, y=2x-3 .. whatever. Just so long as the results are what you are after. Does this make sense? Just ask if not, but basically, what you are looking for is a relationship between two functions. So, in the end, it depends on the question being asked.

#### sby64

Joined Sep 29, 2012
6
Although it may be too late to answer this question yet it may help someone. In my opinion and experience it is always good, easy and practical to get the reference point marked as zero from which you could easily calculate the direction (positive or negative) and the distance to reach your destination. In a two variable system you will be interested in all values of one variable that makes the other zero and unfortunately any value other than that will make life difficult due to a bad reference point. That is also precisely the reason why the reference in electrical/electronic circuit is considered to be at zero potential although it may actually not be truly at zero potential. But it makes life a lot easier.

#### Wendy

Joined Mar 24, 2008
23,320
Congratulations, you have practiced the arcane art of necromancy, the revival of a long dead thread. Likely the OP (Original Poster) has solved his problem in the years that has passed, or thrown it away, or something.

It is usually a good idea to keep it within 6 months of the last post, unless it is your thread.

• tshuck

#### DerStrom8

Joined Feb 20, 2011
2,390 #### sby64

Joined Sep 29, 2012
6
Congratulations, you have practiced the arcane art of necromancy, the revival of a long dead thread. Likely the OP (Original Poster) has solved his problem in the years that has passed, or thrown it away, or something.

It is usually a good idea to keep it within 6 months of the last post, unless it is your thread.

#### WBahn

Joined Mar 31, 2012
29,521
And, to cut a newbie a bit of slack, it is pretty easy to dredge up an old thread without realizing it. When you do a search (or when you try to start a new thread), the forum will present you with results its myopic little mind thinks are relevant. You seldom look at dates as you peruse(sp?) them and are apt to write a reply without thinking to do so. I suspect many of us have done it -- I know I have and more than once.

If it hadn't been for Bill Marsden's note, I would have replied with a different reason why solving for roots is worthwhile, namely it allows you to factor a polynomial into a product of lower order polynomials, which can be quite useful.

#### amilton542

Joined Nov 13, 2010
497
On the contrary, I would just like to point out in that we're not always interested in certain solutions for a quadratic.

For instance, solving trig' equations by means of the squaring method has a tendency to generate an extraneous solution that of which does not hold for the initial condition.

#### Brownout

Joined Jan 10, 2012
2,390
You seldom look at dates as you peruse(sp?) them and are apt to write a reply without thinking to do so.

Yeah, and that date is stinking hard to find. I've been on here for months, and I still have trouble finding it.

#### killivolt

Joined Jan 10, 2010
835
Yeah, and that date is stinking hard to find. I've been on here for months, and I still have trouble finding it.
I don't care about whether or not it was right to pull it out of the Dead Thread Pile.

It's one of those perfect things to read while eating lunch, short and sweet #### electron_prince

Joined Sep 19, 2012
96
you have a equation with a variable and you want to find value that value of variable which satisfies the equation. I mean you want to find that value of variable for which L.H.S = R.H.S. if we have zero on one side, it makes the work quite easy.

#### thatoneguy

Joined Feb 19, 2009
6,359
This thread is a bump magnet, like a super-ball.

• DerStrom8

#### Brownout

Joined Jan 10, 2012
2,390
For what values of X is the bouncing super ball at Y=0?