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For the expansions of (1 + αx)⁴ and (1 - αx)⁶, one value of α that makes the coefficients of their middle terms equal is -3/10. The other possible value of α is

1. 0
2. 1
3. 2
4. 3

Correct answer: 0

Solution

Middle term coeff of (1+ax)^4 is C(4,2)a^2=6a^2; of (1-ax)^6 is C(6,3)(-a)^3=-20a^3. Setting equal: 6a^2+20a^3=0 -> 2a^2(3+10a)=0 -> a=0 or a=-3/10. The other value is 0.

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