Question

The quadratic equation ax² + 20x + c = 0 has exactly one solution. If a + c 29, and a < c find the ordered pair ( a, c)

Answer 1

(a,c) = (4,25)

Explanation:

Since the quadratic equation has exactly one solution, then its discriminant must be 0:

`20^2-4ac=0\\400-4ac=0\\ac=100`

Given that
`a+c=29`, it's easy to see that
`a=4` and
`c=25` since 4*25=100 and 4<25.