The quadratic equation ax^2 + 8x + c = 0 has exactly one solution. If a + c = 12, and a < c, find the ordered pair (a, c).
Hint: Here are the possible values of a and c. Try plugging them in and solving it.
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For one solution thie discriminant of the quadratic = 0 b^2 - 4ac = 0
64 - 4 ac = 0
so another equation relating a and c 64 - 4 ac = ac = 16 and given c = 12-a
a (12-a) = 16
-a^2 + 12a - 16 = 0 quadratic formula shows a = 6 - 2sqrt 5
and c = 6 + 2 sqrt 5