Q. 18

Find a positive value of m for which the coefficient of x2 in the expansion (1 + x)m is 6.

Answer :

The general term Tr+1 in the binomial expansion is given by Tr+1 = nCr an-r br

Here a = 1, b = x and n = m


Putting the value


Tr+1 = mCr 1m-r xr


= mCr xr


We need coefficient of x2


putting r = 2


T2+1 = mC2 x2


The coefficient of x2 = mC2


Given that coefficient of x2 = mC2 = 6




m(m-1) = 12


m2- m - 12 =0


m2- 4m +3m - 12 =0


m(m-4) + 3(m-4) = 0


(m+3)(m - 4)= 0


m = - 3, 4


we need positive value of m so m = 4

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Finding remainder using binomial theoremFinding remainder using binomial theoremFinding remainder using binomial theoremFREE Class
Lecture on properties of Binomial CoefficientsLecture on properties of Binomial CoefficientsLecture on properties of Binomial Coefficients58 mins
Interactive Quiz on properties of Binomial CoefficientsInteractive Quiz on properties of Binomial CoefficientsInteractive Quiz on properties of Binomial Coefficients51 mins
Interactive Quiz | general & middle termsInteractive Quiz | general & middle termsInteractive Quiz | general & middle terms53 mins
Interactive quiz on general and middle terms of binomial theoremInteractive quiz on general and middle terms of binomial theoremInteractive quiz on general and middle terms of binomial theorem54 mins
Learn Binomial Theorem through QuestionsLearn Binomial Theorem through QuestionsLearn Binomial Theorem through Questions52 mins
Learn how to find general & middle termsLearn how to find general & middle termsLearn how to find general & middle terms41 mins
Finding coefficient of x^n in binomial expansionFinding coefficient of x^n in binomial expansionFinding coefficient of x^n in binomial expansion59 mins
Questions based on General term of Binomial TheoremQuestions based on General term of Binomial TheoremQuestions based on General term of Binomial Theorem58 mins
General Term of Binomial TheoremGeneral Term of Binomial TheoremGeneral Term of Binomial Theorem60 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses