- View Source

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

@ rahul ...a^49 -- sum of all rootsa^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 =0i.e, x^2 coeffient is 1x^1 coeffient is - sum of rootsx^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**wrote:*<rahulbhat2000@...>*

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 PMThnx Sachin.....

Got it....

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

RahulOn 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....ThanksRahul.

Your Mail works best with the New Yahoo Optimized IE8. Get it NOW!. - View SourceRahul,Let it reiterate what thing you were narrating in your earlier emaila-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 terseHoping 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??

RahulOn 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....ThanksRahul. - View Source@Sachin & @Revathi...Thanks a ton both of you...Now i have got it properly!!......Thanks again.RahulOn Tue, Mar 23, 2010 at 10:03 AM, Revathi <revathivanga@...> wrote:@ rahul ...

"So the coefiicient will be the same for all ?? a^47,a^46 and so on??""a^49 -- sum of all rootsa^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 =0i.e, x^2 coeffient is 1x^1 coeffient is - sum of rootsx^0 coeffient is --- product of roots (or sum of product of roots two at a time ).... (as equation power is 2 it ended thr.).To: "Sachin K" <sachin.sk@gmail.com>

Cc: ascent4cat@yahoogroups.com

Date: Sunday, 21 March, 2010, 7:40 PMThnx Sachin.....

Got it....

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

RahulOn 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....ThanksRahul.