What is Rooting? What does it mean to have additional roots?

When an equation is deformed, it is sometimes possible to produce roots that are not suitable for the original equation, which is called the additional root of the original equation.

If the root of a fractional equation is such that the common denominator of the equation is zero, then this root is the additional root of the original equation.

Causes of rooting:

For fractional equations, when the value of the denominator is zero in the fractional equation, it is meaningless, so the fractional equation does not allow the unknowns to take those values that make the value of the denominator zero, that is, the fractional equation itself implies the condition that the denominator is not zero. When a fractional equation is converted into an integral equation, this restriction is removed, in other words, the range of unknowns in the equation is expanded, and if the root of the transformed integral equation happens to be a value other than the allowable value of the unknowns of the original equation, then the root addition will occur.

Both sides of the fractional equation are multiplied by the simplest common denominator fractional equation as an integral equation, and the allowable value of the unknown is expanded, so the solution of the fractional equation is prone to root increases.

For example, if you solve a unary equation with x1=-1 x2=0 x3=1

But the question requires x>0

Then x1 x2 is the root increase.

In addition, the calculated value is substituted into the original equation, and the denominator is 0 after the fractional integer, then this root is the increasing root.

Root increase: a mathematical noun that refers to the fact that in the process of transforming a fractional equation into an integral equation, if the root of the integral equation makes the simplest common denominator 0, (the root makes the integral equation true, and the denominator in the fractional equation is 0), then this root is called the additional root of the original fractional equation.

Example: x (x-2)-2 (x-2)=0

Solution: denominator removed, x-2=0

x=2 but x=2 makes the denominator equal to 0 (meaningless), so x=2 is the increment.

The non-negligible nature of rooting:

Many people solve equations and get root additions, for example, energy is a negative value, and most people ignore this, but these values are quite interesting. When the famous physicist Dirac used the theory of relativity and quantum mechanics to find the energy of a particle, he found that the energy of a particle is closely related to its momentum, that is, e 2 = p 2 + m 2 (p is the momentum, m is the mass of the particle), and the solution is e = (p 2 + m 2) (1 2), you must want to keep the positive roots, because you know that the energy will not be negative, but the mathematicians told Dirac that you can't ignore the negative values, because the math tells me that there are two roots, and you can't just throw them away.

It turned out that the second root, the one that is negative, is the crux of the theory: there are both particles and antiparticles in the world. Negative energy is used to explain what antiparticles are.

Substituting the calculated value into the original equation, and solving the denominator is 0 after fractionalization, then this root is the increasing root.

No solution: Look at this equation.

The equation x 2 + x + 1 = 0 is called unsolved

PS: It's also worth noting,"Roots"It's just for unary equations. Multivariate equations can't be called"Roots"It should be called"Solution"

When the equation is deformed, sometimes a root that is not suitable for the original equation may be generated, and this root is called the additional root of the original equation Because the additional root may be produced when solving the fractional equation, the solution of the fractional equation must be tested For the sake of simplicity, the obtained root is usually substituted into the integer (the simplest common denominator) multiplied during the deformation to see if its value is 0, so that the root of the integer 0 is the additional root of the original equation and must be rounded

Resources.

Root increase: Suppose -- for example-- solve a unary equation with x1=-1x2=0x3=1

But the question requires x>0

Then x1 x2 is the root increase.

In addition, the calculated value is substituted into the original equation, and the denominator is 0 after the fractional integer, then this root is the increasing root.

No solution: Look at this equation.

The equation x 2 + x + 1 = 0 is called unsolved

PS: It's also worth noting,"Roots"It's just for unary equations. Multivariate equations can't be called"Roots"It should be called"Solution"

Substituting the fractional equation into the fractional equation where the value of the denominator is 0 or the root of the transformed integral equation happens to be the root of the value other than the allowable value of the unknown of the original equation, it is called the additional root of the original equation.

For example: Set an equation.

a(x)=0

is (x)=0

of the roots, called. x=a

is the addition of the root of the equation; If x=b

is equation b(x)=0

but not a(x)=0

, called x=b

is equation b(x)=0

of lost roots.

The root increment is the value of x that makes the denominator of the original fractional equation zero, for example: 1 3x-3, when x is equal to 1, the denominator is zero, then x=1 is the root increment of the original fractional equation.

Extraneous

root, when the equation is deformed, sometimes a root that is not suitable for the original equation may be generated, that is, the value of the denominator after substituting the fractional equation is 0 or the root of the transformed integral equation happens to be the root of the value other than the allowable value of the unknown of the original equation, which is called the root of the original equation.

Root increment refers to the root obtained after the equation is solved, which does not meet the problem condition. Quadratic equations, fractional equations, and other equations that produce multiple solutions may have additional roots under certain conditions. In the process of converting fractional equations into integral equations, the condition for solving fractional equations is that the denominator of the original equation is not zero.

If the root of an integral equation is such that the simplest common denominator is 0, (the root makes the integral equation true, and in the fractional equation the denominator is 0), then this root is called the incremental root of the original fractional equation.

In a fraction, the denominator is zero and there is no solution to the fraction. It's called root addition.

If, in the process of solving the equation, the range of the roots of the original equation is expanded, a root that is not suitable for the original equation is generated.

Then this root is the additional root of the original equation.

For example: fractional equations. Its original unknowns are in the denominator, and there is a restriction that makes the denominator not equal. But the integer equation with the denominator removed is not very restrictive. This widens the range of values for unknowns, and it is possible to generate additional roots that are not suitable for the original equation.

Therefore, the teacher asked us to solve fractional equations and we had to test the roots.

Because fractional equations are not the same as integral equations.

We solve a fractional equation by removing the denominator, but if the denominator is zero, the original equation is meaningless.

Then if you solve the root and bring it in, you will find that the denominator is zero.

It's the addition of roots, which does not exist in the first place.

Therefore, fractional equations should be tested, and this is the reason.

To put it simply, root addition means that when the fractional equation is solved again, the value of the solved unknown is substituted into the original equation so that the denominator of the original equation is zero, so that the original equation is not valid, and the root addition is generated.

In the process of converting a fractional equation into an integral equation, if the root of the integral equation makes the simplest common denominator 0, (the root makes the integral equation true, while in the fractional equation the denominator is 0), then this root is called the additional root of the original fractional equation.

Adding a root is the value of x that makes the denominator of the original equation zero, which is a basic concept in math books.

In layman's terms, the denominator is 0, and there is no solution to the formula.

If the solution obtained after the deformation of the equation does not conform to the original equation, then this solution is called the root addition of the original equation.

What is the root, 2 minutes to understand what is the rooting of the equation.

The solution of the whole equation obtained after simplification makes the original equation meaningless, and such a solution is called the root addition of the original equation.

The added root represents a solution that conforms to an integral equation but does not conform to a fractional equation, while no solution indicates that the equation has no solution.

Example: (x-1) (x-2)=1, the equation has no solution.

x-1) (x 2-1)=0, after removing the denominator, it becomes x-1=0, and the solution is x=1 but when x=1, the denominator in the fraction will be 0, so x=1 is the root of the equation.

The denominator is zero, in the simplest case.

Increasing the root refers to the root that makes the fractional feast equation meaningless.

For example, fractional equation 2 (x-1)-1 (x-1)=0

According to the solution method of the macro-silver equation, x=1 is solved, but x=1 makes the original equation meaningless, then x=1 is the root increase.