If any quadratic polynomial has real one single root the the discriminant of the quadratic equation is 0.
`f(x) = k`
`x^2+2x+9 = k`
`x^2+2x+(9-k) = 0`
Discriminant `(Delta) = 4-4xx1xx(9-k) = 0`
`4-4xx1xx(9-k) = 0`
`k-9 = -1`
`k = 8`
So for exactly one real root the value of k should be 8.