Division Algorithm in Polynomials | SMO Senior 2024 | Problem 14 | Cheenta | Deepan Dutta

[@joseluishablutzelaceijas928]

Thank you for the problem and its solution. As you are asking for other possible solutions at the end of the video, here an alternative one: From the relation a+b+c = 2, you can deduce that c-1 = 1-a-b, which means that a*b+c-1 = a*b-a-b+1 = (a-1)*(b-1). Therefore, S = 1/((a-1)*(b-1)) + 1/((b-1)*(c-1)) + 1/((c-1)*(a-1)) = (1-c)/((1-a)*(1-b)*(1-c)) + (1-a)/((1-a)*(1-b)*(1-c)) + (1-b)/((1-a)*(1-b)*(1-c)) = (3-(a+b+c))/((1-a)*(1-b)*(1-c)) = 1/((1-a)*(1-b)*(1-c)). Now, given that a, b and c are the roots of 2x^3-4x^2-21x-8 = 2*(x-a)*(x-b)*(x-c), one only needs to evaluate the polynomial at x = 1 and then divide by 2, which results in -31/2. As a result, S = 1/(-31/2) = -2/31 = m/n and m^2+n^2 = 965.

[@Ambal-JEE]

nice solution

[@Deepan_Dutta]

Very nice and simple approach. Keep it up.

[@AnshikaMishra-n9i]

Good video

[@Cheenta]

Thanks