The above question is from the Regents Examination in Algebra I (Common Core) Sample Questions Fall 2013 (link to it from EngageNY's page here).
The big question to the test writers and test takers is this: what are the solutions if the quadratic formula is not used?
Some people may chuckle at this, but it seriously takes into question the skill level of the creators of the test. Admittedly, the method first taught in school is factoring, and that method will not work. However, completing the square will do an admirable job.
In addition, a quick graph on a graphic calculator (which students are required to have) would allow solvers to identify the roots to the nearest integer, then calculate the four choices to see what is reasonable.
Also, with a graphic calculator, one could get a fairly decent decimal approximation and then calculate the choices to see which one "pairs up". I haven't worked with a TI calculator in a few years, but I can pretty much be assured that there are at least 2 or 3 ways of getting decimal approximations to roots (x-intercepts).
In general the question is misleading and poorly written. Imagine a student who is the master of calculators and quadratics who skips this question because they never liked the quadratic formula.
Below is a comparable question from the first of these tests (Regents Examination in Algebra I (Common Core) from June 2014) that was actually used. See the difference? Much better.