Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 124

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\[3x^{2} + 10x + q = 0;\ \ \ x = - 5\]

\[3 \cdot 25 + 10 \cdot ( - 5) + q = 0\]

\[75 - 50 + q = 0\]

\[q = - 25.\]

\[3x^{2} + 10x - 25 = 0\]

\[D_{1} = 100 + 300 = 400\]

\[x_{1} = \frac{- 10 + 20}{6} = \frac{10}{6} = \frac{5}{3};\ \ \]

\[x_{2} = \frac{- 10 - 20}{6} = - 5.\]

\[3x^{2} + 10x - 25 =\]

\[= 3 \cdot \left( x - \frac{5}{3} \right)(x + 5) =\]

\[= (3x - 5)(x + 5).\]