4.3 - NST Substitution

Bestimmung von Nullstellen durch Substitution
Enthält ein Funktionsterm[b] f(x) nur die Potenzen [math]x^2[/math] und [math]x^4[/math] [u]oder[/u] [math]x^3[/math] und [math]x^6[/math] [/b]können die [b]NST [/b]durch [b]Substitution [/b]bestimmt werden. Dafür [b]erstetzt [/b]man [b]jedes[/b] [math]x^2[/math] durch [b]z [/b]und [b]jedes[/b] [math]x^4[/math] entsprechend [b]durch[/b] [math]z^2[/math] (bzw. jedes [math]x^3[/math] durch z und jedes [math]x^6[/math] durch [math]z^2[/math]). [br][b]Die so entstandene [u]quadratische [/u]Funktion f(z) kann mit der pq-Formel gelöst werden! Anschließend können die NST der Ursprungsfunktion durch Wurzelziehen bestimmt werden.[br][br]Bsp. 1:[br][math]f\left(x\right)=x^4-7x^2+12[/math] [/b]der Term enthält nur die Potenzen [math]x^2[/math] und [math]x^4[/math]. Es kann also substituiert werden.[br] setze [math]z=x^2[/math][br][math]f\left(z\right)=z^2-7z+12[/math][br] pq-Formel liefert:[br][math]z_{1,2}=\frac{7}{2}\pm\sqrt{\left(-\frac{7}{2}\right)^2-12}=\frac{7}{2}\pm\sqrt{\frac{1}{4}}=\frac{7}{2}\pm\frac{1}{2}[/math][br][math]z_1=4[/math], [math]z_2=3[/math][br] Rücksubstituieren ([math]z_1=x^2[/math]bzw. [math]z_2=x^2[/math]) liefert:[br]  [math]x^2=z_1\Leftrightarrow x^2=4\Rightarrow x_{1,2}=\pm\sqrt{4}=\pm2[/math][br]  [math]x^2=z_2\Leftrightarrow x^2=3\Rightarrow x_{3,4}=\pm\sqrt{3}[/math][br]also sind die NST von f(x): [math]x_1=2,x_2=-2,x_3=\sqrt{3},x_4=-\sqrt{3}[/math].[br][br][img]data:image/png;base64,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[/img][br][br][b]Bsp. 2:[br][math]g\left(x\right)=x^6-10x^3+9[/math] [/b]der Term enthält nur die Potenzen [math]x^3[/math] und [math]x^6[/math]. Es kann also substituiert werden.[br] setze [math]z=x^3[/math][br][math]g\left(z\right)=z^2-10z+9[/math][br] pq-Formel liefert:[br][math]z_{1,2}=\frac{10}{2}\pm\sqrt{\left(-\frac{10}{2}\right)^2-9}=\frac{10}{2}\pm\sqrt{16}=5\pm4[/math][br][math]z_1=1[/math], [math]z_2=9[/math][br] Rücksubstituieren ([math]z_1=x^3[/math]bzw. [math]z_2=x^3[/math]) liefert:[br]  [math]x^3=z_1\Leftrightarrow x^3=1\Rightarrow x_1=\sqrt[3]{1}=1[/math][br]  [math]x^3=z_2\Leftrightarrow x^3=9\Rightarrow x_2=\sqrt[3]{9}\approx2,08[/math][br]also sind die NST von g(x): [math]x_1=1,x_2=2,08[/math].[br][br][img]data:image/png;base64,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[/img][br]

Information: 4.3 - NST Substitution