The answer depends on assumptions on plaintext.
If an adversary can enumerate the possible plaintext (e.g. if plaintext is a password, mediocre passphrase, or a published file) then yes: knowledge of h1 or h2 allows finding what plaintext is, by verifying beyond reasonable doubt an hypothesis made. For some level of protection against that, use a Password-Based Key Derivation Function such as PBKDF2, or better scrypt.
If plaintext can't be guessed (e.g has 128 bits of entropy), then no: root and plaintext will not leak, from a practical standpoint. More precisely, we are safe, for some strong enough hypothesis on H, that SHA-256 may meet (and meets in practice as far as we know).. or perhaps not (since we have no proof). A suitable hypothesis on H is being computationally indistinguishable from a random function (aside from the length-extension property, and being a particular public function).
As pointed in another answer, we'd have the HMAC security argument if we used
h1 = HMAC( Hash=SHA-256, Key=root, Message=salt1 )
h2 = HMAC( Hash=SHA-256, Key=root, Message=salt2 )