Zero vs. Root: Exploring the Differences

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In summary, the terms "zero" and "root" are often used interchangeably, but there is a technical difference between them when talking about functions and equations. A function has zeroes, which are points in the domain where the function equals zero, while an equation has roots, which are solutions that make the equation equal to zero. However, in common usage, these terms are often used synonymously. It is important to distinguish between the two in order to avoid confusion.
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theperthvan
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What's the difference between a zero and a root?
cheers.
 
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  • #2
For a function, there is none. Basically talking about the roots of a function is a fancy way of speaking about the set of points in the domain where the function takes on the value zero. Though, in other contexts, the word root can make sense whereas zero doesn't (e.g. square root, root system, etc.) -- you'll recognize them when you come across them.
 
  • #3
Technically, an equation has a root while a function has a zero (a "zero" of the function f is a "root" of the equation f(x)= 0). Compuchip is correct that the distinction is not maintained very much but I think it is a shame. The "root" of an equation does not always mean the right side of the equation is "0" and that is the impression that using "root" to mean "zero" of a function gives!
 
  • #4
Thanks. By root I mean (x-3)(x+4)=0 =>x=3,-4. Not square roots or anything.

I just remembered something being said like (x-2)^3 has three roots but only 1 x-intercept, and then another question which I can't find seemed to imply it was the same case with zeroes and roots.
cheers,
 
  • #5
Just had me algebra exam and that was a question!

I pretty much put what HallsofIvy said. I asked the lecturer after and he said that zeroes were to do with the function and roots were an algebraic property.

cheers
 

1. What is the difference between zero and root in mathematics?

Zero and root are two terms used in mathematics to represent different concepts. Zero is a number that represents the absence of quantity or value, while root refers to a number that, when multiplied by itself a certain number of times, gives the original number. In other words, zero is a specific number, while root is a mathematical operation.

2. How are zero and root used in equations?

In equations, zero is often used as a placeholder for unknown values or to represent a starting point. On the other hand, root is used to find unknown values by solving equations. For example, in the equation x^2 = 4, the value of x can be found by taking the square root of both sides, giving us x = 2 or x = -2.

3. Can zero be a root of an equation?

Yes, zero can be a root of an equation. This means that when the equation is solved, the value of the variable will be zero. For example, in the equation x^2 - 4x = 0, the roots are 0 and 4, meaning that when x is equal to 0 or 4, the equation is satisfied.

4. What is the difference between real and imaginary roots?

Real roots are values of a variable that make the equation true when substituted in, while imaginary roots are values that do not make the equation true. Imaginary roots involve the use of imaginary numbers (i) and are often represented by complex numbers. Real roots, on the other hand, are represented by real numbers.

5. How do zero and root relate to the concept of polynomial functions?

Polynomial functions are expressions that involve variables raised to different powers and coefficients. The degree of a polynomial function is determined by the highest power of the variable. The number of roots of a polynomial function is equal to its degree. For example, a polynomial function of degree 3 will have 3 roots, which can be real or imaginary. Zero is also considered a root of a polynomial function since it satisfies the equation when substituted in.

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