Question

All the roots of the polynomial z^6+10z^5+Az^4+Bz³+Cz²+Dz+16 are positive integers, possibly repeated. What is the value of B？

(A)-88
(B)-80
(C) -64
(D) -41
(E) -40

Answer 1

Hi,

-88

Explanation:

6 roots: 1 multiplicity 2

2 multiplicity 4

`P(z)=z^6+10z^5+Az^4+Bz^3+Cz^2+Dz+16 = (z-1)^2*(x-2)^4\\`

Developing P(z) , we find B=-88