--description--

Let $a_n$ be the largest real root of a polynomial $g(x) = x^3 - 2^n \times x^2 + n$.

For example, $a_2 = 3.86619826\ldots$

Find the last eight digits of $\displaystyle\sum_{i = 1}^{30} \lfloor {a_i}^{987654321}\rfloor$.

Note: $\lfloor a\rfloor$ represents the floor function.

--hints--

rootsOfCubicPolynomials() should return 28010159.

assert.strictEqual(rootsOfCubicPolynomials(), 28010159);

--seed--

--seed-contents--

function rootsOfCubicPolynomials() {

  return true;
}

rootsOfCubicPolynomials();

--solutions--

// solution required