PROOF for: P(x) = anxn + an-1xn-1 + 90 HELP

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In summary, the conversation involves a request for help with a proof for the fundamental theorem of algebra using a polynomial P(x) = anxn + an-1xn-1 + ... + 90, and the confusion and lack of clarity surrounding the task. The end goal is to prove that there exists a complex number z = a + bi for which P(z) = 0.
  • #1
Daniel Monroy
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PROOF for: P(x) = anxn + an-1xn-1 + ... 90 HELP!

Homework Statement


P(x) = anxn + an-1xn-1 + ... +90

Homework Equations


1

The Attempt at a Solution


all day...nothing

I need some guidence with this Proof. Google isn't helping much. I have no idea how to do this.
 
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  • #2


I have no idea what you are trying to prove. Can you state the original question?
 
  • #3


I need a proof for

P(x) = anxn + an-1xn-1 + ... +90

related to the fundamental thorem of algebra

if someone could give me wth a proof for the FTA it would be appreciated just as much!
 
  • #4


Proofs of FTA you can find on-line. That doesn't change the fact that P(x) = anxn + an-1xn-1 + ... +90 is not a statement you can prove. Is it supposed to be definition of P(x) or what? What are you supposed to prove?
 
  • #5


I really don't know my proofessor just gave it to me to make up for a missed test what CAN you do with it?... cause i don't know where to start
 
  • #6


I don't think anyone would know where to start. I really think you misunderstood the question. You might ask for clarification.
 
  • #7


ohh well could some one help me prove that Z=a+bi exists?
 
  • #8


We finally figured out that you meant
[tex]P(x)= a_nx^n+ a_{n-1}x^{n-1}+ \cdot\cdot\cdot+ 90[/tex]
but that simply defines a polynomial. It doesn't say anything about the polynomial so there is nothing to be proved.
 
  • #9


I think I finally understand what the OP is trying to say in this and the other thread he has started. Given the polynomial P(x) = anxn + an-1xn-1 + ... + 90, the FTA says that there exists at least one number z = a + bi such that P(z) = 0.

The OP is extremely vague on what he needs to do, but I think he wants to prove the FTA for this polynomial.
 
  • #10


'...90'?? As long as we are playing guessing games, I'm going to take a guess that the '90' is a distorted reading of 'a0'. There's nothing special about that polynomial. The OP must want a general proof of the FTA.
 

Related to PROOF for: P(x) = anxn + an-1xn-1 + 90 HELP

What is the purpose of "PROOF for: P(x) = anxn + an-1xn-1 + 90 HELP"?

The purpose of this equation is to find the value of the polynomial function P(x) given its coefficients and the constant term 90.

How do you solve this equation?

To solve this equation, you can use algebraic methods such as factoring, synthetic division, or the quadratic formula. You can also use a graphing calculator or computer software to find the roots of the equation.

What does the "anxn + an-1xn-1" part of the equation represent?

The terms "anxn" and "an-1xn-1" represent the coefficients of the polynomial function. The coefficient "an" is multiplied by the variable x raised to the nth power, while the coefficient "an-1" is multiplied by the variable x raised to the (n-1)th power.

Is there a specific method for solving this type of equation?

There is no specific method for solving this type of equation, as it depends on the specific coefficients and constant term given. However, there are general algebraic methods and tools that can be used to solve polynomial equations.

How do I know if my solution is correct?

To check if your solution is correct, you can plug in the values of the coefficients and the constant term into the original equation and see if it satisfies the equation. You can also use a graphing calculator or computer software to graph the equation and see if the roots match your solution.

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