Question

If the sum of the coefficient in the expansion of `(alpha^2x^2-2alphax+1)^(51)` vanishes, then find the value of`alpha`

Answer 1

We have `(alpha^(2)x^(2)-3alphax+2)^(51)`.
`:.` Sum of coefficients `= (alpha^(2)-3alpha+2)^(51)`
Since sum of coefficient is zero,
`alpha^(2) - 3alpha + 2 =0`
`rArr (alpha+2)(alpha-1)=0`
`rArr alpha = 1,2`