Why do we equal equations to 0 (zero)?

  • Thread starter Leo Duluc
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In summary, the conversation discusses the concept of equaling equations to zero and why it is done. It is explained that manipulating equations in this way helps to make them easier to read and solve, and also allows for the determination of critical points and graphing. It is also mentioned that setting polynomials equal to zero helps to find the x-intercept or point where y=0 on the graph. Overall, it is a useful technique for solving equations and graphing functions.
  • #1
Leo Duluc
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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.
 
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  • #2
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
 
  • #3
Leo Duluc said:
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.
 
  • #4
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!
 
  • #5
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.
 
  • #6
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.
 
  • #7
thanks

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

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The scientific method is a systematic approach to conducting and analyzing experiments. It involves making observations, formulating a hypothesis, designing and conducting experiments, collecting and analyzing data, and drawing conclusions.

Why is the scientific method important?

The scientific method allows for a systematic and objective approach to understanding the natural world. It helps scientists avoid biases and errors, and ensures that their findings are reliable and replicable.

How do scientists determine the cause of a phenomenon?

Scientists use the scientific method to test their hypotheses and gather evidence to support or refute their explanations for a phenomenon. They conduct controlled experiments, gather data, and use statistical analyses to determine the cause of a phenomenon.

What are some limitations of the scientific method?

The scientific method relies on empirical evidence and can only explain phenomena that can be observed and measured. It also does not provide definitive answers and is subject to human biases and errors.

How does the scientific method contribute to our understanding of the world?

The scientific method allows for the accumulation of knowledge and the advancement of scientific theories. It also helps us make informed decisions and solve real-world problems based on evidence rather than assumptions.

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