Finding original algebraic equation

  • Thread starter -EquinoX-
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In summary, the original polynomial should have factors of (x - (a + bi))(x - (a - bi)) or (x2 - 2ax + a2 + b2). If the degree of the polynomial is larger than 2, there will be other roots. To find the original polynomial, multiply (x - (a + bi))(x - (a - bi)) and set it equal to 0. The resulting polynomial will have a2 + b2 as one of its terms.
  • #1
-EquinoX-
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1

Homework Statement



if I have a root of a +/- bi

i = imaginary number

what should the original algebra eqution?


Homework Equations





The Attempt at a Solution

 
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  • #2
The original polynomial should have factors of (x - (a + bi))(x - (a - bi)), or equivalently, a single factor of (x2 - 2ax + a2 + b2). If the degree of the polynomial you're working with is larger than 2, there will be other roots, as well.
 
  • #3
x- (a+ bi) and x- (a- bi) are factors. Multiply [itex](x- (a+bi))(x- (a- bi)= ((x-a)- bi)((x-a)+bi)= (x-a)^2+ b^2[/itex] and set it equal to 0.
 
  • #4
thanks Mark, shouldn't it be a^2 - b^2?
 
  • #5
-EquinoX- said:
thanks Mark, shouldn't it be a^2 - b^2?
Nope. The a2 + b2 comes from multiplying (-(a + bi))(-(a - bi)) = (a + bi)(a - bi) = a2 -b2i2 = a2 + b2.
 

What is the process for finding the original algebraic equation?

The process for finding the original algebraic equation involves reverse engineering a given equation to determine the original form. This typically involves using algebraic techniques such as factoring, expanding, and simplifying.

How do you know if an equation is the original form?

An equation is considered the original form if it cannot be further simplified or factored. This means that all of the terms and coefficients are in their most simplified form and there are no common factors remaining.

What are some common techniques used to find the original algebraic equation?

Some common techniques used to find the original algebraic equation include factoring, expanding, completing the square, and using the quadratic formula. These techniques are based on algebraic principles and can help to simplify and rearrange equations to their original form.

Can an equation have multiple original forms?

Yes, an equation can have multiple original forms. This is because there are often different ways to manipulate and rearrange an equation to its simplest form. However, all of these forms will ultimately be equivalent and represent the same relationship between variables.

Is it always possible to find the original algebraic equation?

No, it is not always possible to find the original algebraic equation. This is especially true for more complex equations with higher degrees and multiple variables. In some cases, the original form may be lost or impossible to determine due to the manipulation and simplification of the equation.

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