text: # Solve the Polynomial Inequality
  
  • Jun 17th 2013, 04:47 PM
  AceBoogie
  Solve the Polynomial Inequality
  I threw this equation into Mathway, but the answer wasn't correct. I have two tries at the question, so looking for some help. The equation is as follows:
  
  (x-10)(x+3)(x-2)^2 < 0
  
  Any suggestions?
  • Jun 17th 2013, 05:08 PM
  chiro
  Re: Solve the Polynomial Inequality
  Hey AceBoogie.
  
  Hint: Try looking at values left and right of the zeroes (i.e. 10, -3, and 2) and see when you get a negative or a positive answer.
  
  Then use this to get the regions when < 0 and you're done. (For example if f(x) = (x-10)(x+3)(x-2)^2 and f(1) < 0 then the interval [-3,2] is <= 0 since 1 is between -3 and 2).
  • Jun 17th 2013, 05:16 PM
  AceBoogie
  Re: Solve the Polynomial Inequality
  I think I am trying to set up the equation so the x values will make the equation = 0. In this case would the answer be:
  
  (-3,2)U(2,10)?
  • Jun 17th 2013, 05:31 PM
  Plato
  Re: Solve the Polynomial Inequality
  Quote:
  
  Originally Posted by AceBoogie
  I threw this equation into Mathway, but the answer wasn't correct. I have two tries at the question, so looking for some help. The equation is as follows:
  
  (x-10)(x+3)(x-2)^2 < 0
  
  I have a different take on this.
  
  Because \$\displaystyle (x-2)^2\ge 0\$ the only case we cannot have x=2 .
  
  So we need \$\displaystyle (x-10)(x+3)<0\$ with \$\displaystyle x\ne 2\$
explanation: The document is a forum thread where a user named AceBoogie posts a math question about solving a polynomial inequality. The inequality in question is \((x-10)(x+3)(x-2)^2 < 0\). Other users, including chiro and Plato, provide hints and suggestions to help solve the inequality. The thread contains a question and multiple responses, but no definitive answer is provided by the original poster.
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: # Solve the Polynomial Inequality
  
  • Jun 17th 2013, 04:47 PM
  AceBoogie
  Solve the Polynomial Inequality
  I threw this equation into Mathway, but the answer wasn't correct. I have two tries at the question, so looking for some help. The equation is as follows:
  
  (x-10)(x+3)(x-2)^2 < 0
  
  Any suggestions?
  • Jun 17th 2013, 05:08 PM
  chiro
  Re: Solve the Polynomial Inequality
  Hey AceBoogie.
  
  Hint: Try looking at values left and right of the zeroes (i.e. 10, -3, and 2) and see when you get a negative or a positive answer.
  
  Then use this to get the regions when < 0 and you're done. (For example if f(x) = (x-10)(x+3)(x-2)^2 and f(1) < 0 then the interval [-3,2] is <= 0 since 1 is between -3 and 2).
  • Jun 17th 2013, 05:16 PM
  AceBoogie
  Re: Solve the Polynomial Inequality
  I think I am trying to set up the equation so the x values will make the equation = 0. In this case would the answer be:
  
  (-3,2)U(2,10)?
  • Jun 17th 2013, 05:31 PM
  Plato
  Re: Solve the Polynomial Inequality
  Quote:
  
  Originally Posted by AceBoogie
  I threw this equation into Mathway, but the answer wasn't correct. I have two tries at the question, so looking for some help. The equation is as follows:
  
  (x-10)(x+3)(x-2)^2 < 0
  
  I have a different take on this.
  
  Because \$\displaystyle (x-2)^2\ge 0\$ the only case we cannot have x=2 .
  
  So we need \$\displaystyle (x-10)(x+3)<0\$ with \$\displaystyle x\ne 2\$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a forum thread where a user named AceBoogie posts a math question about solving a polynomial inequality. The inequality in question is \((x-10)(x+3)(x-2)^2 < 0\). Other users, including chiro and Plato, provide hints and suggestions to help solve the inequality. The thread contains a question and multiple responses, but no definitive answer is provided by the original poster.
  
  Label: question-and-answer