شاه کلید نکات
شاه کلید سوال
1 با توجّه به فعالیت بالا، جاهای خالی را با عبارت های مناسب پر کنید.
2 معادله های زیر را با فرمول کلی حل کنید.
الف \({x^2} - x + 1 = 0\)
ب \( - 2{x^2} + x + 3 = 0\)
پ \( - {x^2} + 4x - 4 = 0\)
الف
\(\begin{array}{*{20}{l}}\begin{array}{l}{x^2} - x + 1 = 0\\\\ \Rightarrow \left\{ {\begin{array}{*{20}{l}}{a = 1}\\{b = - \,1}\\{c = 1}\end{array}} \right.\\\\ \Rightarrow \Delta = {b^2} - 4ac = {\left( { - \,1} \right)^2} - 4\left( 1 \right)\left( 1 \right) = - 3 < 0\end{array}\end{array}\)
جواب ندارد
ب
\(\begin{array}{*{20}{l}}\begin{array}{l} - 2{x^2} + x + 3 = 0\\\\ \Rightarrow \left\{ {\begin{array}{*{20}{l}}{a = - \,2}\\{b = \,1}\\{c = 3}\end{array}} \right.\\\\ \Rightarrow \Delta = {b^2} - 4ac = {\left( 1 \right)^2} - 4\left( { - 2} \right)\left( 3 \right) = 25\\\end{array}\\{x = \frac{{ - b \pm \sqrt \Delta }}{{2a}} = \frac{{ - 1 \pm 5}}{{ - 4}} \Rightarrow \left\{ {\begin{array}{*{20}{l}}\begin{array}{l}{x_1} = \frac{3}{2}\\\end{array}\\{{x_2} = - 1}\end{array}} \right.}\end{array}\)
پ
\(\begin{array}{*{20}{l}}\begin{array}{l} - {x^2} + 4x - 4 = 0\\\\ \Rightarrow \left\{ {\begin{array}{*{20}{l}}{a = - 1}\\{b = \,4}\\{c = - 4}\end{array}} \right.\\\\ \Rightarrow \Delta = {b^2} - 4ac = {\left( 4 \right)^2} - 4\left( { - 1} \right)\left( { - 4} \right) = 0\\\end{array}\\{x = \frac{{ - b}}{{2a}} = \frac{{ - 4}}{{ - 2}} = 2}\end{array}\)
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