Consider the polynomial f(x)=17x4+21x3+60x2+Ax+B. Suppose that for every root λ of f(x)=0, 1/λ is also a root of f(x)=0. What is the value of A+B?

Answer 1

If two of the roots are m and n,

f(x) = (x-m)(x-n)(mx-1)(nx-1)

B = mn
17 = mn
so, B=17

mn*1/m + mn*1/n + m*1/m*1/n + n*1/m*1/n = -A/17

n + m + 1/m + 1/n = -A/17

But, we also know that the sum of the roots is -21/17, so

A = 21

A+B = 38

As it happens, all he roots are complex, but they are reciprocals in pairs!

Answer 2

Hmmm. Getting B is ill written.
B/17 = product of all roots
m*n*1/m*1/n = 1
B/17 = 1
B = 17