The coefficient of the middle term in the binomial expansion in powers of `x` of`(1+alphax)^4` and of`(1-alphax)^6` is the same, if `alpha` equals

Question

The coefficient of the middle term in the binomial expansion in powers of `x` of`(1+alphax)^4` and of`(1-alphax)^6` is the same, if `alpha` equals

The coefficient of the middle term in the binomial expansion in powers of `x` of`(1+alphax)^4` and of`(1-alphax)^6` is the same, if `alpha` equals
A. `-5/3`
B. `10/3`
C. `-3/10`
D. `3/5`

Monjur Alahi

8 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - C
Middle term of `(1+alphax)^(4)` is `T_(3)`.
Its coefficient is `.^(4)C_(2)(alpha)^(2)=6alpha^(2)`.
Middle term of `(1-alphax)^(6)` is `T_(4)`.
Its coefficient is `.^(6)C_(3) (-alpha)^(3) = -20alpha^(3)`.
According to question.
`6alpha^(2) = - 20 alpha^(3)`
or `3alpha^(2)+ 10alpha^(3) = 0`
or `alpha^(2) (3+10alpha) = 0`
or `alpha = -3/10`