text: # Math
  
  posted by .
  
  For what values of k will the functon f(x)=kx^2-4x+k have no zeros
  
  Determine the values of k for which the function f(x)=4x^2-3x+2kx+1 have 2 zeros
  
  • Math -
  
  if b^2 - 4ac < 0 ---> no real zeros
  if b^2 - 4ac = 0 ---> one real zero
  ifb^2 - 4ac > 0 ---> two real zeros
  
  if will do the 2nd question.
  a=4, b= 2k-3 , c = 1
  
  b^2 - 4ac
  = (2k-3)^2 - 4(4)(1)
  = 4k^2 - 12k + 9 - 16
  = 4k^2 - 12k - 7
  = (k + 1)(4k - 7)
  
  (k+1)(4k-7) > 0 for 2 real roots
  k < -1 OR k > 7/4
explanation: The document contains two math questions related to quadratic functions and their zeros. The first question asks for the values of \( k \) for which the function \( f(x) = kx^2 - 4x + k \) has no zeros. The second question asks for the values of \( k \) for which the function \( f(x) = 4x^2 - 3x + 2kx + 1 \) has two zeros. The document also provides a detailed solution for the second 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: # Math
  
  posted by .
  
  For what values of k will the functon f(x)=kx^2-4x+k have no zeros
  
  Determine the values of k for which the function f(x)=4x^2-3x+2kx+1 have 2 zeros
  
  • Math -
  
  if b^2 - 4ac < 0 ---> no real zeros
  if b^2 - 4ac = 0 ---> one real zero
  ifb^2 - 4ac > 0 ---> two real zeros
  
  if will do the 2nd question.
  a=4, b= 2k-3 , c = 1
  
  b^2 - 4ac
  = (2k-3)^2 - 4(4)(1)
  = 4k^2 - 12k + 9 - 16
  = 4k^2 - 12k - 7
  = (k + 1)(4k - 7)
  
  (k+1)(4k-7) > 0 for 2 real roots
  k < -1 OR k > 7/4
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains two math questions related to quadratic functions and their zeros. The first question asks for the values of \( k \) for which the function \( f(x) = kx^2 - 4x + k \) has no zeros. The second question asks for the values of \( k \) for which the function \( f(x) = 4x^2 - 3x + 2kx + 1 \) has two zeros. The document also provides a detailed solution for the second question.
  
  Label: multiple-question-and-answer