Why do we equal equations to 0 (zero)?

[Leo Duluc]

ok, this may be a stupid cuestion, but it has gotten me very curious, and if somebody could help with it, I would appreciated very much thanks.

Ok here it goes, why do we equal equations to 0 (zero) for example (quadratics ones) y don’t understand why, I have some ideas but I don’t know if they are right, what I thought is that what they do is put every term on one side of the equations, if it so, why do they do this, what’s the reason.

Thank's.

 

[chroot]

You can take any equation at all and manipulate it until one side equals zero. You can move terms from one side to the other by adding or substracting to both sides. Polynomials, for example, are conventionally represented this way, simply to make them easier to read.

The solutions of such equations are often called the "zeroes" of the equation.

- Warren

 

[Chrono]

Ok here it goes, why do we equal equations to 0 (zero) for example (quadratics ones) y don’t understand why, I have some ideas but I don’t know if they are right, what I thought is that what they do is put every term on one side of the equations, if it so, why do they do this, what’s the reason.

Also, and Warren or somebody correct me if I'm wrong, putting the equations equal to 0, it helps us to sketch the graph of that function. For example, setting the derivatives of a function equal to zero finds the critical points of that function, which determine the points on the graph where the function curves.

 

[Tide]

Putting a function, e.g. a polynomial, into the form of P(x) = 0 emphasizes the fact that when the polynomial is written as a product of factors then it must be that one or more of those factors must be zero in order for the statement to be true. It's very useful, in fact!

 

[HallsofIvy]

It isn't necessary to move all the terms to one side of an equation in order to solve it. For example, to solve the equation x²+ 2x= 7 , I would notice immediately that x²+ 2x+ 1 is a perfect square (it is (x+1)²) and so add 1 to both sides (completing the square). x²+ 2x+ 1= 8 so
(x+1)²= 8 and then solve by taking the square root.

IF you want to solve an equation by factoring, the simplest way to solve a polynomial equation (when it is possible), uses the fact that if xy= 0 then either x or y must be 0, as Tide said. That is not true if xy= any number other than 0.

 

[Didd]

Hello, Leo Duluc!
This point is touched in the above post but let me repeat it again in slightly different way.

The reason to set polynomials,in general, specifically like, linear, quadratic and etc... equal to zero helps us to find where the graph touches the x-axis, the point where the value of y=0,or x-intercept. This will enable us to draw a graph without going further of constructing tables and some thing like that.

I hope this helps. You may find it interesting in the future.

 

[Leo Duluc]

thanks

Thank you very much everybody you have clarified everything, you have been very helpful, and I thank you again.