Let m and n be the roots of 7x^2 + 9x + 21 = 0. Find (m + 7)(n + 7).
Using the quadratic formula, we get:
m=[ -0.6428571429 +1.608332893 i] + 7 = [6.35714 + 1.60833 i ] n=[ -0.6428571429 -1.608332893 i ] + 7 = [6.35714 - 1.60833 i ]
[6.35714 + 1.60833 i ] * [6.35714 - 1.60833 i ] = ~43
7x^2 + 9x + 21 = 0
And
( m + 7)(n + 7) = (mn)^2 + 7 (m + n) + 49 (1)
By Vieta,
m + n = - 9/7 (2)
mn = 21/7 = 3 square both sides
(mn)^2 = 9 (3)
Sub (2) and (3) into (1) and we have that
(m + 7) ( n +7) = (9) + 7(-9/7) + 49 = 49
