Question 1017603
If *[tex \large x^2 + mx + 1] has roots p and q, then *[tex \large p+q = -m] and *[tex \large pq = 1].


Then the roots of *[tex \large x^2 + nx + m] are 2p and 2q, and *[tex \large 2p+2q = -n] and *[tex \large 4pq = m].


Since *[tex \large pq = 1], we have *[tex \large m = 4pq = 4]. Then *[tex \large p+q = -m = -4], and *[tex \large n = -(2p+2q) = -(-8) = 8].