The quadratic equation ax^2+32x+c=0 has exactly one solution. If a+c=130, and a>c, find the ordered pair (a, c).

Ie 32^2 - 4ac=0 so ac=256 and a+c=130

So, that means:2 equations ac=256 a+c=130 ie c=130-a

So, a (130-a) = 256 so 130a - a^2=256 ie a^2-130a + 256=0 (a-2) (a-128) = 0

Finally, giving a = 2 or a=128 so, a=2 c=128 or a=128 c=2

Since, a>c, a=128 and c=2 ie (128,2)