شاه کلید نکات
شاه کلید سوال
همهٔ صفرهای تابع \(f\left( x \right) = {x^3} - 10{x^2} + 16\) را به دست آورید.
\(\begin{array}{*{20}{l}}\begin{array}{l}f\left( x \right) = {x^4} - 10{x^2} + 16\\\\ \Rightarrow {x^4} - 10{x^2} + 16 = 0\\\\ \Rightarrow t = {x^2} \Rightarrow {t^2} - 10t + 16 = 0\end{array}\\\begin{array}{l}\\\Delta = {b^2} - 4ac = {\left( { - 10} \right)^2} - 4\left( 1 \right)\left( {16} \right)\\ = 100 - 64 = 36\end{array}\\\begin{array}{l}\\t = \frac{{ - b \pm \sqrt \Delta }}{{2a}} = \frac{{10 \pm 6}}{2}\\\\ \Rightarrow \left\{ {\begin{array}{*{20}{l}}{{t_1} = 8 \Rightarrow {x^2} = 8 \Rightarrow x = \pm 2\sqrt 2 }\\{{t_2} = 2 \Rightarrow {x^2} = 2 \Rightarrow x = \pm \sqrt 2 }\end{array}} \right.\\\\ \Rightarrow \left\{ {\begin{array}{*{20}{l}}{{x_1} = - \sqrt 2 }\\{{x_2} = \sqrt 2 }\\{{x_3} = - 2\sqrt 2 }\\{{x_4} = 2\sqrt 2 }\end{array}} \right.\end{array}\end{array}\)
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