Chemotherapy and Radiation Therapy (RT) With or Without Vandetanib in Treating Patients With High-Risk Stage III or Stage IV Head and Neck Cancer

DISEASE CHARACTERISTICS: * Histologically or cytologically confirmed squamous cell carcinoma of the head and neck, including any of the following subtypes: * Oral cavity * Oropharynx * Larynx * Hypopharynx * Stage III or IV disease (no distant metastases) * No cancer of the lip, nasopharynx, or sinuses * Must have undergone gross total resection\* (with curative intent) within 3-6 weeks of registration, with pathology demonstrating 1 or more of the following risk factors: * Histologic extracapsular nodal extension * Invasive cancer seen on microscopic evaluation of the resection margin, when all visible tumor has been removed NOTE: \*Tonsillar cancer patients who undergo transoral excision of all gross tumor are eligible if the patient has formal neck dissection confirming histologic extracapsular nodal extension PATIENT CHARACTERISTICS: Inclusion criteria: * Zubrod performance status 0-1 * ANC (absolute neutrophil count) ≥ 2,000/mm³ * Platelet count ≥ 100,000/mm³ * Hemoglobin ≥ 8.0 g/dL (transfusion or other intervention to achieve this level allowed) * Total bilirubin normal * AST (aspartate aminotransferase) or ALT (alanine amino transferase) ≤ 2 times upper limit of normal (ULN) * Alkaline phosphatase ≤ 2.5 times ULN * Serum creatinine ≤ 1.5 mg/dL * Creatinine clearance ≥ 60 mL/min * Glucose ≥ 40 mg/dL AND ≤ 250 mg/dL * Sodium ≥ 130 mmol/L AND ≤ 155 mmol/L * Magnesium ≥ 0.9 mg/dL AND ≤ 3 mg/dL (supplementation allowed) * Potassium ≥ 4 mmol/L AND ≤ 6 mmol/L (supplementation allowed) * Serum calcium (ionized or adjusted for albumin) ≥ 7 mg/dL AND ≤ 12.5 mg/dL (supplementation allowed) * QTc (corrected QT interval) interval ≥ 480 msec must have 2 additional EKGs ≥ 24 hrs apart and the average QTc from the 3 screening EKGs must be \< 480 msec * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for at least 60 days after completion of study treatment * May not donate blood during the study or for 3 months after last dose of vandetanib Exclusion criteria: * Other simultaneous primary cancer * Prior invasive malignancy (except nonmelanoma skin cancer) unless disease free for a minimum of 3 years with the exception of the following: * Carcinoma in situ of the cervix * Adequately treated basal cell or squamous cell carcinoma of the skin * Untreated or treated low-risk prostate cancer (defined as clinical or pathologic T1c, N0 M0, PSA (prostate-specific antigen) \< 10, Gleason \< 7, \< 50% of the total cores positive for cancer) * Severe, active co-morbidity, defined as follows: * Clinically significant cardiovascular event (e.g., myocardial infarction, superior vena cava syndrome, or New York Heart Association class II-IV) or presence of cardiac disease that, in the opinion of the investigator, increases the risk of ventricular arrhythmia within the past 3 months * Unstable angina and/or congestive heart failure requiring hospitalization within the past 3 months * Transmural myocardial infarction within the past 3 months * History of arrhythmia (e.g., multifocal premature ventricular contractions, bigeminy, trigeminy, ventricular tachycardia, or uncontrolled atrial fibrillation) which is symptomatic or requires treatment (CTCAE \[Common Terminology Criteria for Adverse Events\] grade 3), or asymptomatic sustained ventricular tachycardia * Patients with atrial fibrillation, controlled on medication, are eligible * Presence of left bundle branch block * Previous history of QTc prolongation as a result from other medication that required discontinuation of that medication * Congenital long QTc syndrome or first degree relative with unexplained sudden death under 40 years of age * QTc with Bazett's correction that is unmeasurable or ≥ 480 msec on screening EKG * Patients who are receiving a drug that has a risk of QTc prolongation are not eligible if QTc is ≥ 460 msec * Hypertension (systolic blood pressure \[BP\] \> 160 mm Hg or diastolic BP \> 100 mm Hg) not controlled by medical therapy * Diarrhea ≥ grade 1 (increase of \< 4 stools per day over baseline or mild increase in ostomy output compared to baseline) * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration * Chronic obstructive pulmonary disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy within the past 30 days * Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects * Acquired Immune Deficiency Syndrome (AIDS) based upon current CDC (Center for Disease Control) definition (no HIV testing is required for study entry) * Prior allergic reaction to cisplatin or vandetanib or derivatives similar to these drugs PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No prior systemic chemotherapy for this disease (prior chemotherapy for a different cancer allowed) * No prior radiotherapy to the head and neck area that would result in overlap of radiotherapy fields * More than 30 days since prior investigational agents * More than 3 weeks since prior major surgery and recovered * More than 2 weeks since prior and no concurrent medications that induce Torsades de Pointes * More than 2 weeks since prior and no concurrent known potent inducers of CYP3A4 (Cytochrome P450 3A4), including rifampicin, phenytoin, carbamazepine, barbiturates, and Hypericum perforatum (St. John wort) * No concurrent medication that may cause QTc prolongation