Given: y2 + 6y + 9 = 0
To find the nature of the roots, we need to find the discriminant of the given quadratic equation.
We know that the discriminant of a quadratic equation is Δ = b2 – 4ac.
On comparing the given equation with ay2 + by + c= 0 in variable y, we get:
a = 1, b = 6 and c = 9.
Thus,
Δ = (6)2 – 4(1)(9)
=> Δ = 36 – 36 = 0
Since Δ = 0, the roots of the given quadratic equation are real and equal.