text: ## nickersia 2 years ago Medal to first who explains me this question :) Find the roots of the equation (comment).
  
  1. nickersia
  
  \[x ^{3}-x ^{2}-7x+3\]
  
  2. shelbygt520
  
  k whats the question
  
  3. shelbygt520
  
  ok do you want it factorized or what?
  
  4. nickersia
  
  That's problem, I'm not quite sure what should I do :s
  
  5. shelbygt520
  
  x^3+x^2-7x-3 One of the roots is x(1) = -3 After applying Polynomial remainder theorem you will have a second order equation x^2 - 2x - 1 = 0 a = 1 ; b = -2 ; c = -1 x(2,3) = (-b)(+/-)SqRoot{b^2 - 4 . a . c}/(2 a)= x(2,3) = (2)(+/-)SqRoot{4 - 4 . 1 . (-1)}/(2 . 1)= x(2,3) = (2)(+/-)SqRoot{4 + 4}/(2)= x(2,3) = 2 (+/-) SqRoot { 8 } / 2 = x(2,3) = 1 (+/-) SqRoot { 2 } ---> x(2) = 1 + SqRoot { 2 } ---> x(3) = 1 - SqRoot { 2 }
  
  6. shelbygt520
  
  u should do that but instead of doing minus you do the addition this was a mere example but close enough so that you would know what to do
  
  7. nickersia
  
  I understand second part perfectly that's not problem :) can you just explain how did you get -3 as one of the roots? I'm bit confused
  
  8. shelbygt520
  
  I just replaced +3 with -3 in this example
  
  9. shelbygt520
  
  so in your case the root would be +3
  
  10. nickersia
  
  Why is that?
  
  11. shelbygt520
  
  capish? :)
explanation: The document is a conversation from an educational platform where a user named nickersia is seeking help with a math problem. The problem is to find the roots of the polynomial equation \(x^3 - x^2 - 7x + 3\). Another user, shelbygt520, provides a detailed solution, explaining how to find the roots, including the use of the Polynomial Remainder Theorem and the quadratic formula. The conversation also includes a follow-up question from nickersia about how one of the roots was determined.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: ## nickersia 2 years ago Medal to first who explains me this question :) Find the roots of the equation (comment).
  
  1. nickersia
  
  \[x ^{3}-x ^{2}-7x+3\]
  
  2. shelbygt520
  
  k whats the question
  
  3. shelbygt520
  
  ok do you want it factorized or what?
  
  4. nickersia
  
  That's problem, I'm not quite sure what should I do :s
  
  5. shelbygt520
  
  x^3+x^2-7x-3 One of the roots is x(1) = -3 After applying Polynomial remainder theorem you will have a second order equation x^2 - 2x - 1 = 0 a = 1 ; b = -2 ; c = -1 x(2,3) = (-b)(+/-)SqRoot{b^2 - 4 . a . c}/(2 a)= x(2,3) = (2)(+/-)SqRoot{4 - 4 . 1 . (-1)}/(2 . 1)= x(2,3) = (2)(+/-)SqRoot{4 + 4}/(2)= x(2,3) = 2 (+/-) SqRoot { 8 } / 2 = x(2,3) = 1 (+/-) SqRoot { 2 } ---> x(2) = 1 + SqRoot { 2 } ---> x(3) = 1 - SqRoot { 2 }
  
  6. shelbygt520
  
  u should do that but instead of doing minus you do the addition this was a mere example but close enough so that you would know what to do
  
  7. nickersia
  
  I understand second part perfectly that's not problem :) can you just explain how did you get -3 as one of the roots? I'm bit confused
  
  8. shelbygt520
  
  I just replaced +3 with -3 in this example
  
  9. shelbygt520
  
  so in your case the root would be +3
  
  10. nickersia
  
  Why is that?
  
  11. shelbygt520
  
  capish? :)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a conversation from an educational platform where a user named nickersia is seeking help with a math problem. The problem is to find the roots of the polynomial equation \(x^3 - x^2 - 7x + 3\). Another user, shelbygt520, provides a detailed solution, explaining how to find the roots, including the use of the Polynomial Remainder Theorem and the quadratic formula. The conversation also includes a follow-up question from nickersia about how one of the roots was determined.
  
  Label: question-and-answer