MathNet 2007-part-03 — 185 problems (EN–VI) Question 42

If the polynomial $$f(x) = x^6 + a_1 x^5 + a_2 x^4 + a_3 x^3 + a_4 x^2 + a_5 x + 3$$ with real coefficients possesses all negative roots, show that $f(2) \ge 27^2$.