text: # Quadratic equation
  
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  • Oct 19th 2008, 04:29 PM
  B-lap
  Quadratic equation
  The equation: x^3 - 3x^2 - 10x + 24 = 0
  
  has roots: 2, "h" and "k"
  
  Determine a quadratic equation whose roots are "h" - "k" and "hk"
  
  How do you do it?
  
  The anwser is: x^2 + 5x -84 = 0
  • Oct 19th 2008, 05:38 PM
  terr13
  I'm guessing that you can solve for h and k, by first dividing by x-2, and the factoring the resulting polynomial. Say that h = 3 and k = -4. Then h-k = 3-(-4) = 7. hk = -12. Create the two polynomials corresponding to the roots.
  (x-7)(x+12). Multiply it out to get the answer.
  
  (I didn't solve the polynomial, I worked backwards to get the answer, but the approach is the same.)
explanation: The document contains a math problem involving a cubic equation and its roots. It asks for the quadratic equation whose roots are derived from the given roots of the cubic equation. The document also includes an answer to the question.
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: # Quadratic equation
  
  Printable View
  
  • Oct 19th 2008, 04:29 PM
  B-lap
  Quadratic equation
  The equation: x^3 - 3x^2 - 10x + 24 = 0
  
  has roots: 2, "h" and "k"
  
  Determine a quadratic equation whose roots are "h" - "k" and "hk"
  
  How do you do it?
  
  The anwser is: x^2 + 5x -84 = 0
  • Oct 19th 2008, 05:38 PM
  terr13
  I'm guessing that you can solve for h and k, by first dividing by x-2, and the factoring the resulting polynomial. Say that h = 3 and k = -4. Then h-k = 3-(-4) = 7. hk = -12. Create the two polynomials corresponding to the roots.
  (x-7)(x+12). Multiply it out to get the answer.
  
  (I didn't solve the polynomial, I worked backwards to get the answer, but the approach is the same.)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math problem involving a cubic equation and its roots. It asks for the quadratic equation whose roots are derived from the given roots of the cubic equation. The document also includes an answer to the question.
  
  Label: question-and-answer