For $y'' + by' + ky = 0$ (a damped oscillator), the roots of the characteristic equation are complex with negative real part. Without solving anything else, what does the solution do?

C. It oscillates while decaying to zero

Complex roots mean oscillation; a negative real part wraps it in a shrinking exponential envelope, underdamped ringing, like a struck bell. The root locations are a complete qualitative dictionary: no solution formula needed.