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Updated Mar 19, 2026

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解と係数の関係を学ぼう

2次方程式や3次方程式の解と係数の間には、実はとても便利な関係があるんだ。この関係を理解すると、複雑な計算をしなくても解の和や積を簡単に求められるようになる。

解と係数の関係

解と係数の関係は、方程式の解を直接求めなくても、解同士の和や積が分かってしまう超便利な公式だ。テストでも頻出だから、しっかりマスターしよう。

2次方程式 ax² + bx + c = 0 の2つの解をα、βとすると：

解の和：α + β = -b/a
解の積：αβ = c/a

3次方程式 ax³ + bx² + cx + d = 0 の3つの解をα、β、γとすると：

α + β + γ = -b/a
αβ + βγ + γα = c/a
αβγ = -d/a

💡 ポイント！ 係数の符号に注意！解の和は常に最高次の項の次の係数に-1をかけて最高次の係数で割ったものだよ。

この公式を覚えておけば、解の値が分数や無理数になる複雑な方程式でも、解の和や積をパッと計算できる。計算ミスも減らせるから一石二鳥だね。

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Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

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Marco B

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Paul T

iOS user

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Updated Mar 19, 2026

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解と係数の関係を学ぼう

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解と係数の関係

2次方程式 ax² + bx + c = 0 の2つの解をα、βとすると：

解の和：α + β = -b/a
解の積：αβ = c/a

3次方程式 ax³ + bx² + cx + d = 0 の3つの解をα、β、γとすると：

α + β + γ = -b/a
αβ + βγ + γα = c/a
αβγ = -d/a

💡 ポイント！ 係数の符号に注意！解の和は常に最高次の項の次の係数に-1をかけて最高次の係数で割ったものだよ。