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Re: [2IIM CAT Prep] Coefficient of a^48

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  • Revathi
    So the coefiicient will be the same for all ?? a^47,a^46 and so on?? @ rahul ...   a^49 -- sum of all roots  a^48 -- sum of (product of two roots at a
    Message 1 of 6 , Mar 22, 2010
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      "So the coefiicient will be the same for all ?? a^47,a^46 and so on??""
      @ rahul ...
       
      a^49 -- sum of all roots
       a^48 -- sum of (product of two roots at a time).
      a^47 -- sum of product of 3 roots at a time .
      .... (if sign should consider then alternative + and _ signs from a^50).
       
      for Eg : (x-k1)(x-k2) = 0 is equation in variable x and k1, k2 are roots ( as like a is var & 1,2 are roots in the above equation) then equation is x^2 - (k1+k2)x+k1k2 =0
       
      i.e, x^2 coeffient is 1
            x^1 coeffient is - sum of roots
            x^0 coeffient is --- product of roots (or sum of product of roots two at a time ).... (as equation power is 2 it ended thr.).      
           


      --- On Sun, 21/3/10, Rahul Bhat <rahulbhat2000@...> wrote:

      From: Rahul Bhat <rahulbhat2000@...>
      Subject: Re: [2IIM CAT Prep] Coefficient of a^48
      To: "Sachin K" <sachin.sk@...>
      Cc: ascent4cat@yahoogroups.com
      Date: Sunday, 21 March, 2010, 7:40 PM

       
      Thnx Sachin.....

      Got it....

      So the coefiicient will be the same for all ?? a^47,a^46 and so on??

      Rahul

      On Sun, Mar 21, 2010 at 12:30 PM, Sachin K <sachin.sk@gmail.com> wrote:
      Hey Rahul,
       
      I will detail out the procedure here for you..

      Any expression like this is a polynomial in 'a'.. and the numbers within the bracket (e.g. 1, 2, 3, ...50) are the roots of this polynomial in 'a', and you can also write this polynomial in its expsnaded form as:
       
      (a-1)(a-2)(a- 3)......( a-50) = (a^50) - (SUM_OF_ROOTS) *(a^49) + (SUM_OF_ALL_ PRODUCT_OF_ TWO_ROOTS) *(a^48) - ....... + (PRODUCT_OF_ ROOTS).
       
      So, You can see yourself that the coefficient of a^48 is nothing but the "SUM_OF_ALL_PRODUCT_ OF_TWO_ROOTS".
       
      Answer =  (1.2 + 1.3 + 1.4 + ... + 1.50) + (2.3 + 2.4 + .... + 2.50) + (3.4 + ... +3.50) + ...+ (48.49 + 48.50) + (49.50).
       
      GOT IT !!
       
       
      --Sachin Kumar
      ============ ========= ========= ========= ========= ========= =========
      On Thu, Mar 18, 2010 at 1:55 PM, Rahul Bhat <rahulbhat2000@ gmail.com> wrote:
       
      Hey guyz..
       
      how to find out the Coefficient of a^48 in (a-1)(a-2)(a- 3)......( a-50)??
       
      Plz explain the answer with the method....
       
      Thanks
      Rahul.




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    • hardev Parmar
      Rahul, Let it reiterate what thing you were narrating in your earlier email a-1)(a-2)(a- 3)......( a-50) = (a^50) - (SUM_OF_ROOTS) *(a^49) + (SUM_OF_ALL_
      Message 2 of 6 , Mar 24, 2010
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        Rahul,
         
        Let it reiterate what thing you were narrating in your earlier email
         
        a-1)(a-2)(a- 3)......( a-50) = (a^50) - (SUM_OF_ROOTS) *(a^49) + (SUM_OF_ALL_ PRODUCT_OF_ TWO_ROOTS) *(a^48) - ....... + (PRODUCT_OF_ ROOTS).
         
        Muddle in Aforementioned line. pls make it terse  


        Hoping for a positive response

        Thanks & Regards,
        Hardev



        From: Rahul Bhat <rahulbhat2000@...>
        To: Sachin K <sachin.sk@...>
        Cc: ascent4cat@yahoogroups.com
        Sent: Sun, March 21, 2010 6:10:56 AM
        Subject: Re: [2IIM CAT Prep] Coefficient of a^48

         

        Thnx Sachin.....

        Got it....

        So the coefiicient will be the same for all ?? a^47,a^46 and so on??

        Rahul

        On Sun, Mar 21, 2010 at 12:30 PM, Sachin K <sachin.sk@gmail.com> wrote:
        Hey Rahul,
         
        I will detail out the procedure here for you..

        Any expression like this is a polynomial in 'a'.. and the numbers within the bracket (e.g. 1, 2, 3, ...50) are the roots of this polynomial in 'a', and you can also write this polynomial in its expsnaded form as:
         
        (a-1)(a-2)(a- 3)......( a-50) = (a^50) - (SUM_OF_ROOTS) *(a^49) + (SUM_OF_ALL_ PRODUCT_OF_ TWO_ROOTS) *(a^48) - ....... + (PRODUCT_OF_ ROOTS).
         
        So, You can see yourself that the coefficient of a^48 is nothing but the "SUM_OF_ALL_PRODUCT_ OF_TWO_ROOTS".
         
        Answer =  (1.2 + 1.3 + 1.4 + ... + 1.50) + (2.3 + 2.4 + .... + 2.50) + (3.4 + ... +3.50) + ...+ (48.49 + 48.50) + (49.50).
         
        GOT IT !!
         
         
        --Sachin Kumar
        ============ ========= ========= ========= ========= ========= =========
        On Thu, Mar 18, 2010 at 1:55 PM, Rahul Bhat <rahulbhat2000@ gmail.com> wrote:
         

        Hey guyz..
         
        how to find out the Coefficient of a^48 in (a-1)(a-2)(a- 3)......( a-50)??
         
        Plz explain the answer with the method....
         
        Thanks
        Rahul.




      • Rahul Bhat
        @Sachin & @Revathi... Thanks a ton both of you...Now i have got it properly!!...... Thanks again. Rahul
        Message 3 of 6 , Apr 1 1:11 AM
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          @Sachin & @Revathi...
           
          Thanks a ton both of you...Now i have got it properly!!......
           
          Thanks again.
           
          Rahul

          On Tue, Mar 23, 2010 at 10:03 AM, Revathi <revathivanga@...> wrote:
           


          "So the coefiicient will be the same for all ?? a^47,a^46 and so on??""
          @ rahul ...
           
          a^49 -- sum of all roots
           a^48 -- sum of (product of two roots at a time).
          a^47 -- sum of product of 3 roots at a time .
          .... (if sign should consider then alternative + and _ signs from a^50).
           
          for Eg : (x-k1)(x-k2) = 0 is equation in variable x and k1, k2 are roots ( as like a is var & 1,2 are roots in the above equation) then equation is x^2 - (k1+k2)x+k1k2 =0
           
          i.e, x^2 coeffient is 1
                x^1 coeffient is - sum of roots
                x^0 coeffient is --- product of roots (or sum of product of roots two at a time ).... (as equation power is 2 it ended thr.).      
               


          --- On Sun, 21/3/10, Rahul Bhat <rahulbhat2000@...> wrote:

          From: Rahul Bhat <rahulbhat2000@...>
          Subject: Re: [2IIM CAT Prep] Coefficient of a^48
          To: "Sachin K" <sachin.sk@gmail.com>
          Cc: ascent4cat@yahoogroups.com
          Date: Sunday, 21 March, 2010, 7:40 PM


           
          Thnx Sachin.....

          Got it....

          So the coefiicient will be the same for all ?? a^47,a^46 and so on??

          Rahul

          On Sun, Mar 21, 2010 at 12:30 PM, Sachin K <sachin.sk@gmail.com> wrote:
          Hey Rahul,
           
          I will detail out the procedure here for you..

          Any expression like this is a polynomial in 'a'.. and the numbers within the bracket (e.g. 1, 2, 3, ...50) are the roots of this polynomial in 'a', and you can also write this polynomial in its expsnaded form as:
           
          (a-1)(a-2)(a- 3)......( a-50) = (a^50) - (SUM_OF_ROOTS) *(a^49) + (SUM_OF_ALL_ PRODUCT_OF_ TWO_ROOTS) *(a^48) - ....... + (PRODUCT_OF_ ROOTS).
           
          So, You can see yourself that the coefficient of a^48 is nothing but the "SUM_OF_ALL_PRODUCT_ OF_TWO_ROOTS".
           
          Answer =  (1.2 + 1.3 + 1.4 + ... + 1.50) + (2.3 + 2.4 + .... + 2.50) + (3.4 + ... +3.50) + ...+ (48.49 + 48.50) + (49.50).
           
          GOT IT !!
           
           
          --Sachin Kumar
          ============ ========= ========= ========= ========= ========= =========
          On Thu, Mar 18, 2010 at 1:55 PM, Rahul Bhat <rahulbhat2000@ gmail.com> wrote:
           
          Hey guyz..
           
          how to find out the Coefficient of a^48 in (a-1)(a-2)(a- 3)......( a-50)??
           
          Plz explain the answer with the method....
           
          Thanks
          Rahul.




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