text: # Resolve 12x3+3x2−3x−2 into partial fractions:
  
  Video Solution
  Text Solution
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  ## We have, 12x3+3x2−3x−2=1(x−1)(x+2)(2x+1) Let 12x2+3x2−3x−2=A(x−1)+Bx+2+C2x1. Then, ⇒1=A(x+2)(2x+1)+B(x−1)(2x+1)+C(x−1)(x+)…………..(i) Putting x−1=0 or x=1 in (i), we get ⇒A=19 Putting x=−2, in (i), we obtain B=19 Putting x=−12in (i), we obtain C=−49 ∴12x3+3x2−3x−2=1(x−1)(x+2)(2x+1)=19(x−1)+19(x+2)−49(2x+1)
  
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  Updated on:21/07/2023
  
  ### Knowledge Check
  
  • Question 1 - Select One
  
  ## Resolve x−1x3−3x2+2x into partical fractions.
  
  A1(x2)12x
  B12(x2)12x
  C1(x2)+1x1+12x
  D1(x2)1x1+12x
  • Question 2 - Select One
  
  ## Resolve 1x4−3x2−4 into partical fractions.
  
  A15(x24)+15(x2+1)
  B15(x24)15(x2+1)
  C14(x2+4)14(x2+1)
  D14(x2+4)+14(x2+1)
  • Question 3 - Select One
  
  ## Resolve x(x−2)(x2+3)2 into partial fractions.
  
  A149[2x22x+4x2+3+122x(x2+3)2]
  B149[2x22x+4x2+3122x(x2+3)2]
  C149[2x2+2x+4x2+3122x(x2+3)2]
  D149[2x22x+4x2+3+2114x(x2+3)2]
  
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  Doubtnut is the perfect NEET and IIT JEE preparation App. Get solutions for NEET and IIT JEE previous years papers, along with chapter wise NEET MCQ solutions. Get all the study material in Hindi medium and English medium for IIT JEE and NEET preparation
explanation: The provided text extract contains a math question and its detailed solution. The question is about resolving a given polynomial expression into partial fractions. The solution is provided step-by-step, including the values of the constants and the final form of the partial fractions.
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distilabel_metadata.content: # Resolve 12x3+3x2−3x−2 into partial fractions:
  
  Video Solution
  Text Solution
  Verified by Experts
  
  ## We have, 12x3+3x2−3x−2=1(x−1)(x+2)(2x+1) Let 12x2+3x2−3x−2=A(x−1)+Bx+2+C2x1. Then, ⇒1=A(x+2)(2x+1)+B(x−1)(2x+1)+C(x−1)(x+)…………..(i) Putting x−1=0 or x=1 in (i), we get ⇒A=19 Putting x=−2, in (i), we obtain B=19 Putting x=−12in (i), we obtain C=−49 ∴12x3+3x2−3x−2=1(x−1)(x+2)(2x+1)=19(x−1)+19(x+2)−49(2x+1)
  
  |
  Updated on:21/07/2023
  
  ### Knowledge Check
  
  • Question 1 - Select One
  
  ## Resolve x−1x3−3x2+2x into partical fractions.
  
  A1(x2)12x
  B12(x2)12x
  C1(x2)+1x1+12x
  D1(x2)1x1+12x
  • Question 2 - Select One
  
  ## Resolve 1x4−3x2−4 into partical fractions.
  
  A15(x24)+15(x2+1)
  B15(x24)15(x2+1)
  C14(x2+4)14(x2+1)
  D14(x2+4)+14(x2+1)
  • Question 3 - Select One
  
  ## Resolve x(x−2)(x2+3)2 into partial fractions.
  
  A149[2x22x+4x2+3+122x(x2+3)2]
  B149[2x22x+4x2+3122x(x2+3)2]
  C149[2x2+2x+4x2+3122x(x2+3)2]
  D149[2x22x+4x2+3+2114x(x2+3)2]
  
  Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board, Rajasthan Board, MP Board, Telangana Board etc
  NCERT solutions for CBSE and other state boards is a key requirement for students. Doubtnut helps with homework, doubts and solutions to all the questions. It has helped students get under AIR 100 in NEET & IIT JEE. Get PDF and video solutions of IIT-JEE Mains & Advanced previous year papers, NEET previous year papers, NCERT books for classes 6 to 12, CBSE, Pathfinder Publications, RD Sharma, RS Aggarwal, Manohar Ray, Cengage books for boards and competitive exams.
  Doubtnut is the perfect NEET and IIT JEE preparation App. Get solutions for NEET and IIT JEE previous years papers, along with chapter wise NEET MCQ solutions. Get all the study material in Hindi medium and English medium for IIT JEE and NEET preparation
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text extract contains a math question and its detailed solution. The question is about resolving a given polynomial expression into partial fractions. The solution is provided step-by-step, including the values of the constants and the final form of the partial fractions.
  
  Label: question-and-answer