Question

the sum of coefficients of f(x) if 16x^16-11x+2×f(x) =2016x^2015
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Answer 1

Answer:

let's say f(x) = ax^n+bx^m....

to find the sum of the coefficients we need to substitute x = 1 so that we will get the sum of the coefficients.

coming back to the question if we substitute x = 1 in (16x^16-11x+2)× f(x) = 2016x^2015

we will get ,

(16(1)^16 -11(1) +2)× f(1) = 2016

.•. f(1) = 2016/7 = 288

so, the sum of the coefficients of f(x) = 288

Answer 2

Given : {16x⁶-11x+2}f(x) =2016.x²⁰¹⁵

To find : Sum of the coefficient of f(x)

Solution:

f(x) =aₙxⁿ + aₙ₋₁xⁿ⁻¹  + . + .  + a₁x  + a₀  

x = 1

=> f(1) = aₙ  + aₙ₋₁   + . + .  + a₁   + a₀  

Hence f(1) = Sum of the coefficient of f(x)

{16x⁶-11x+2}f(x) =2016.x²⁰¹⁵

substitute x = 1

=> {16 -11 +2}f(1) =2016

=> 7f(1) = 2016

=>  f(1) =  288

Sum of the coefficient of f(x)   = 288

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