One value of α for which the coefficients of the middle terms in the expansion of (1+α x)4 and (1-α x)6 are equal, is (-3/10) . Other value of ' α ' is

Question

One value of α for which the coefficients of the middle terms in the expansion of (1+α x)4 and (1-α x)6 are equal, is (-3/10) . Other value of ' α ' is (A) 0 (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

In the expansion of (1+α x)4 Middle term = 4 C 2(α x )2=6 α2 x 2 In the expansion of (1-α x)6 Middle term = 6 C 3(-α x )3=-20 α3 x 3 It is given that Coefficient of the middle term in (1+α x)4 = Coefficient of the middle term in (1-α x)6 ⇒ 6 α2=-20 α3 ⇒ α=0, α=-(3/10)

Q. One value of α for which the coefficients of the middle terms in the expansion of (1+αx)4 and (1−αx)6 are equal, is 10−3​. Other value of ' α ' is

0

1

2

3

In the expansion of (1+αx)4 Middle term =4C2​(αx)2=6α2x2 In the expansion of (1−αx)6 Middle term =6C3​(−αx)3=−20α3x3 It is given that Coefficient of the middle term in (1+αx)4 = Coefficient of the middle term in (1−αx)6 ⇒6α2=−20α3 ⇒α=0,α=−103​

Q. One value of $α$ for which the coefficients of the middle terms in the expansion of $(1 + αx)^{4}$ and $(1 - αx)^{6}$ are equal, is $\frac{- 3}{10} .$ Other value of ' $α$ ' is