2022-01-21 01:00:18 +05:30
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---
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id: 5900f4d01000cf542c50ffe3
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2022-01-22 20:38:20 +05:30
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title: '問題 356: 三次多項式の最大根'
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2022-01-21 01:00:18 +05:30
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challengeType: 5
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forumTopicId: 302016
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dashedName: problem-356-largest-roots-of-cubic-polynomials
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---
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# --description--
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2022-01-22 20:38:20 +05:30
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$a_n$ を、多項式 $g(x) = x^3 - 2^n \times x^2 + n$ の最大の実根とします。
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2022-01-21 01:00:18 +05:30
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2022-01-22 20:38:20 +05:30
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例: $a_2 = 3.86619826\ldots$
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2022-01-21 01:00:18 +05:30
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2022-01-22 20:38:20 +05:30
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$\displaystyle\sum_{i = 1}^{30} \lfloor {a_i}^{987654321}\rfloor$ の下位 8 桁を求めなさい。
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2022-01-21 01:00:18 +05:30
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2022-01-22 20:38:20 +05:30
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**注:** $\lfloor a\rfloor$ は床関数を表します。
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2022-01-21 01:00:18 +05:30
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# --hints--
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2022-01-22 20:38:20 +05:30
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`rootsOfCubicPolynomials()` は `28010159` を返す必要があります。
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2022-01-21 01:00:18 +05:30
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```js
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assert.strictEqual(rootsOfCubicPolynomials(), 28010159);
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```
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# --seed--
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## --seed-contents--
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```js
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function rootsOfCubicPolynomials() {
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return true;
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}
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rootsOfCubicPolynomials();
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```
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# --solutions--
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```js
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// solution required
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```
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