In the following, you are given the product pq and the sum p + q. Determine p and q:
pq = –44 and p + q = –7
p + q = –7
⇒p = –7–q
putting the value of q in other equation,
⇒ pq = –44
⇒ (–7–q)q = –44
⇒–7q–q2 = –44
⇒q2 + 7q–44 = 0
⇒q2 + 11q–4q–44 = 0
⇒q(q + 11)–4(q + 11) = 0
⇒ (q–4)(q + 11) = 0
so, q = 4 & q = –11
as, p = –7–q
thus, p = –7–4 & p = –7 + 11
p = –11 & p = 4
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