Question
f(x) is a cubic polynomial such that f(n)=1/n^2+1 for n=1,2,3,4. If f(0)=a/b,where a and b are coprime positive integers, what is the value of a+b
Answers
Steve
f(x) = ax^3 + bx^2 + cx + d
f(1) = 1/2
f(2) = 1/5
f(3) = 1/10
f(4) = 1/17
a+b+c+d = 1/2
8a+4b+2c+d = 1/5
27a+9b+3c+d = 1/10
64a+16b+4c+d = 1/17
f(x) = 1/170 (-4x^3 + 41x^2 - 146x + 194)
f(1) = 1/2
f(2) = 1/5
f(3) = 1/10
f(4) = 1/17
a+b+c+d = 1/2
8a+4b+2c+d = 1/5
27a+9b+3c+d = 1/10
64a+16b+4c+d = 1/17
f(x) = 1/170 (-4x^3 + 41x^2 - 146x + 194)