If you want the file to be valid JSON, you have to open your file, parse the JSON, append your new result to the array, transform it back into a string and save it again.
var fs = require('fs')
var currentSearchResult="example"
fs.readFile('results.json', function (err, data) {
var json = JSON.parse(data)
json.push('search result: ' + currentSearchResult)
fs.writeFile("results.json", JSON.stringify(json))
})