Question

5
Find the value of n, if f(x) = 2x^2n - 4x^n - 5 has a remainder of 11 when divided
by 2x - 1​

Answer 1

f(x)=2x*2n-4x*n-5

when f(x)÷2x-1,

the remainder=f(1/2)

f(1/2)=11

2(1/2)*2n-4(1/2)*n-5=11

1*2n-2*n-5=11

-2*n=11+5[any power of 1=1]

(-1)2*n=16

(-1)2*n=2*4

(-1)n=4[because equal base]

-n=4

n=-4