Question

When the function f(x)=2x^n+ax^2-6 is divided by (x-1), the reminder is -7 and when divided by (x+3), the reminder is 129.calculate the value of "a" and "n" and hence write the polynomial function completely

Answer 1

[AI-generated answer — Bot GPT 3.5]

When the function f(x) = 2x^n + ax^2 - 6 is divided by (x - 1), the remainder is given as -7. This means that f(1) = -7.

f(1) = 2(1)^n + a(1)^2 - 6
=> 2 + a - 6 = -7
=> a - 4 = -7
=> a = -3

When the function f(x) = 2x^n + ax^2 - 6 is divided by (x + 3), the remainder is given as 129. This means that f(-3) = 129.

f(-3) = 2(-3)^n + a(-3)^2 - 6
=> 2(-3)^n + 9a - 6 = 129
=> 2(-3)^n + 9a = 135
=> -6(-3)^n + 27a = 270
=> 2(-3)^n + 9a = 135

We know that a = -3, substituting this in the equation:

2(-3)^n + 9(-3) = 135
=> 2(-3)^n - 27 = 135
=> 2(-3)^n = 162
=> (-3)^n = 81
=> n = 4

Therefore, the value of 'a' is -3 and 'n' is 4. The polynomial function completely will be:

f(x) = 2x^4 - 3x^2 - 6