Question

if f(x) is polynomial if degree 'n' such that sum of the coefficients of even power of x is equal to the sum of the coefficients of odd power of x, then
1) f(1) = 0
2) f(-1)= 0
3) f(2) = 0
4) f(3)= 0​

Answer 1

Answer:

0.5(f(1)+f(-1))

Step-by-step explanation:

f(x)=a0+a1*x^1+....+an*x^n

n is odd

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

f(-1)=a0-a1+a2+.................+a(n-2)-a(n-1)

f(1)+f(-1)=2(sum of coefficients of even powers of x)

sum of even coefficients of x=0.5(f(1)+f(-1))

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