The coefficient of the middle term in the binomial expansion in powers of x of (1+αx)4 and of (1−αx)6 is the same, if α equals
A
−53
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B
103
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C
−310
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D
35
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Solution
The correct option is C−310 Middle term of (1+αx)4 is T3. Its coefficient is 4C2(α)2=6α2. Middle term of (1−αx)6 is T4. Its coefficient is 6C3(−α)3=−20α3. According to question, 6α2=−20α3 ⇒3α2+10α3=0 ⇒α2(3+10α)=0 ⇒α=−310