Check sibling questions

Ex 8.2, 12 - Find m for which coefficient of x2 in (1 + x)m

Ex 8.2,12 - Chapter 8 Class 11 Binomial Theorem - Part 2
Ex 8.2,12 - Chapter 8 Class 11 Binomial Theorem - Part 3


Transcript

Ex 8.2, 12 Find a positive value of m for which the coefficient of x2 in the expansion (1 + x)m is 6. We know that General term of expansion (a + b)n is Tr+1 = nCr an–r br General term of (1 + x)m is Putting n = m, a = 1, b = x Tr + 1 = mCr (1)m-r . (x)r = mCr (1) . (x)r = mCr xr We need coefficient of x2 So putting r = 2 Tr + 2 = mC2 x2 Coefficient of x2 is mC2 It is given that coefficient of x2 is 6 i.e. mC2 = 6 π‘š!/2!(π‘š βˆ’ 2)! = 6 (π‘š(π‘š βˆ’ 1)(π‘š βˆ’ 2)!)/2!(π‘š βˆ’ 2)! = 6 (π‘š (π‘š βˆ’ 1))/2 = 6 m (m – 1) = 12 m2 – m = 12 m2 – m – 12 = 0 m2 – 4m + 3m – 12 = 0 m(m – 4) + 3 (m – 4) = 0 (m + 3) (m – 4) = 0 So, m = –3 or m = 4 But we need positive value of m Hence, m = 4

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.