Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 321

\[\boxed{\mathbf{321}.}\]

\[x^{3} + x^{2} + ax + b = 0;\ \ \]

\[x_{1} = 3;\ \ x_{2} = - 4:\]

\[P(3) = 27 + 9 + 3a + b =\]

\[= 36 + 3a + b = 0;\]

\[P( - 4) = - 64 + 16 - 4a + b =\]

\[= - 48 - 4a + b = 0.\]

\[\left\{ \begin{matrix} 3a + b = - 36\ \ \\ - 4a + b = 48\ \ \\ \end{matrix} \right.\ ( - )\]

\[7a = - 84\]

\[a = - 12.\]

\[b = 48 + 4a = 48 - 48 = 0.\]

\[\left\{ \begin{matrix} a = - 12 \\ b = 0\ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[x^{3} + x^{2} - 12x = 0\]

\[x\left( x^{2} + x - 12 \right) = 0\]

\[x(x - 3)(x + 4) = 0.\]

\[Ответ:a = - 12;\ \ b = 0;\ \ x_{3} = 0.\]