{"id":11314,"date":"2019-07-26T13:50:43","date_gmt":"2019-07-26T10:50:43","guid":{"rendered":"http:\/\/mathland.gr\/?p=11314"},"modified":"2019-07-26T13:50:43","modified_gmt":"2019-07-26T10:50:43","slug":"%cf%80%ce%b1%cf%81%ce%b1%ce%b3%ce%bf%ce%bd%cf%84%ce%bf%cf%80%ce%bf%ce%af%ce%b7%cf%83%ce%b7-%cf%84%cf%81%ce%b9%cf%89%ce%bd%cf%8d%ce%bc%ce%bf%cf%85","status":"publish","type":"post","link":"https:\/\/dpanagiotis.sites.sch.gr\/?p=11314","title":{"rendered":"\u03a0\u03b1\u03c1\u03b1\u03b3\u03bf\u03bd\u03c4\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7 \u03a4\u03c1\u03b9\u03c9\u03bd\u03cd\u03bc\u03bf\u03c5"},"content":{"rendered":"

\u03a4\u03b7\u03bd \u03b1\u03bb\u03b3\u03b5\u03b2\u03c1\u03b9\u03ba\u03ae \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \"\alpha x^2+\beta x +\gamma\" \u03c3\u03c5\u03bd\u03ae\u03b8\u03c9\u03c2 \u03c4\u03b7\u03bd \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03c5\u03bc\u03b5 \u03c4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf \u03ba\u03b1\u03b9 \u03bd\u03bf\u03bc\u03af\u03b6\u03c9 \u03cc\u03c4\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03c1\u03bf\u03c6\u03b1\u03bd\u03ae\u03c2 \u03bf \u03bb\u03cc\u03b3\u03bf\u03c2 \u03b1\u03c6\u03bf\u03cd \u03cc\u03c0\u03c9\u03c2 \u03b2\u03bb\u03ad\u03c0\u03bf\u03c5\u03bc\u03b5 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03af\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03c1\u03b5\u03b9\u03c2 \u03bc\u03cc\u03bd\u03bf \u03cc\u03c1\u03bf\u03c5\u03c2. \u03a4\u03bf\u03bd \u03b4\u03b5\u03c5\u03c4\u03b5\u03c1\u03bf\u03b2\u03ac\u03b8\u03bc\u03b9\u03bf \u03cc\u03c1\u03bf “\u03b1x2<\/sup>“, \u03c4\u03bf\u03bd \u03c0\u03c1\u03c9\u03c4\u03bf\u03b2\u03ac\u03b8\u03bc\u03b9\u03bf \u03cc\u03c1\u03bf “\u03b2x” \u03ba\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03cc \u03cc\u03c1\u03bf “\u03b3”.<\/p>\n

\u0393\u03b9\u03b1 \u03c4\u03bf \u03c4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03be\u03b1\u03bd\u03b1\u03bc\u03b9\u03bb\u03ae\u03c3\u03b5\u03b9 \u03c3\u03b5 \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03bf \u03ac\u03c1\u03b8\u03c1\u03bf \u03ba\u03b9 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03b1\u03c3\u03c7\u03bf\u03bb\u03b7\u03b8\u03b5\u03af \u03bc\u03b5 \u03c4\u03bf \u03c0\u03c9\u03c2 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bc\u03b5 \u03bd\u03b1 \u03b2\u03c1\u03bf\u03cd\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03bf\u03c5, \u03b8\u03c5\u03bc\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03bf\u03c5 \u03c4\u03c1\u03b9\u03c9\u03bd\u03cd\u03bc\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03bb\u03cd\u03c3\u03b5\u03b9\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7\u03c2 <\/p>\n

  <\/span>   <\/span>\"\[\alpha x^2+\beta x +\gamma=0\]\"<\/p>\n

(\u03b1\u03bd \u03b8\u03ad\u03bb\u03b5\u03c4\u03b5 \u03bd\u03b1 \u03c4\u03bf \u03b4\u03b9\u03b1\u03b2\u03ac\u03c3\u03b5\u03c4\u03b5 \u03b1\u03bd\u03b1\u03bb\u03c5\u03c4\u03b9\u03ba\u03ac \u03ba\u03ac\u03bd\u03c4\u03b5 \u03ba\u03bb\u03b9\u03ba \u03b5\u03b4\u03ce \u03b1\u03bd \u03b8\u03ad\u03bb\u03b5\u03c4\u03b5 \u03bd\u03b1 \u03b8\u03c5\u03bc\u03b7\u03b8\u03b5\u03af\u03c4\u03b5 \u03c3\u03c4\u03b1 \u03b3\u03c1\u03ae\u03b3\u03bf\u03c1\u03b1 \u03c4\u03b7 \u03b4\u03b9\u03b1\u03b4\u03b9\u03ba\u03b1\u03c3\u03af\u03b1 \u03ba\u03ac\u03bd\u03c4\u03b5 \u03ba\u03bb\u03b9\u03ba \u03b5\u03b4\u03ce \u03bd\u03b1 \u03b4\u03b5\u03af\u03c4\u03b5 \u03c4\u03b7 \u03bc\u03b5\u03b8\u03bf\u03b4\u03bf\u03bb\u03bf\u03b3\u03af\u03b1). \u03a4\u03ce\u03c1\u03b1 \u03b8\u03b1 \u03b1\u03c3\u03c7\u03bf\u03bb\u03b7\u03b8\u03bf\u03cd\u03bc\u03b5 \u03bc\u03b5 \u03c4\u03bf \u03c0\u03c9\u03c2 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bc\u03b5 \u03bd\u03b1 \u03c0\u03b1\u03c1\u03b1\u03b3\u03bf\u03bd\u03c4\u03bf\u03c0\u03bf\u03b9\u03ae\u03c3\u03bf\u03c5\u03bc\u03b5 \u03ad\u03bd\u03b1 \u03c4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae \u03bc\u03b5 \u03c0\u03bf\u03b9\u03bf \u03c4\u03c1\u03cc\u03c0\u03bf \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bc\u03b5 \u03bd\u03b1 \u03bc\u03b5\u03c4\u03b1\u03c4\u03c1\u03ad\u03c8\u03bf\u03c5\u03bc\u03b5 \u03ad\u03bd\u03b1 \u03c4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf \u03c3\u03b5 \u03b3\u03b9\u03bd\u03cc\u03bc\u03b5\u03bd\u03bf. \u0393\u03b9\u03b1 \u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03b1\u03b3\u03bf\u03bd\u03c4\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7 \u03b3\u03b5\u03bd\u03b9\u03ba\u03ac \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03b1\u03bd\u03b1\u03c6\u03b5\u03c1\u03b8\u03b5\u03af \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03b1 \u03b5\u03b4\u03ce<\/a>. \u0395\u03c0\u03b5\u03b9\u03b4\u03ae \u03cc\u03bc\u03c9\u03c2 \u03c3\u03c4\u03bf \u03c3\u03c7\u03bf\u03bb\u03b9\u03ba\u03cc \u03b2\u03b9\u03b2\u03bb\u03af\u03bf \u03b7 \u03c0\u03b1\u03c1\u03b1\u03b3\u03bf\u03bd\u03c4\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c4\u03c1\u03b9\u03c9\u03bd\u03cd\u03bc\u03bf\u03c5 \u03c0\u03b1\u03c1\u03bf\u03c5\u03c3\u03b9\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c1\u03ba\u03b5\u03c4\u03ac \u03b1\u03c1\u03b3\u03cc\u03c4\u03b5\u03c1\u03b1, \u03b4\u03b5\u03bd \u03c4\u03bf \u03b5\u03af\u03c7\u03b1\u03bc\u03b5 \u03b1\u03bd\u03b1\u03c6\u03ad\u03c1\u03b5\u03b9 \u03ba\u03b1\u03b8\u03cc\u03bb\u03bf\u03c5 \u03c4\u03cc\u03c4\u03b5.<\/p>\n

\u0388\u03c6\u03c4\u03b1\u03c3\u03b5 \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd \u03b7 \u03ce\u03c1\u03b1 \u03bd\u03b1 \u03b1\u03c3\u03c7\u03bf\u03bb\u03b7\u03b8\u03bf\u03cd\u03bc\u03b5 \u03ba\u03b1\u03b9 \u03bc\u03b5 \u03b1\u03c5\u03c4\u03cc \u03c4\u03bf \u03b8\u03ad\u03bc\u03b1. \u038c\u03c4\u03b1\u03bd \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd \u03b3\u03b9\u03b1 \u03ba\u03ac\u03c0\u03bf\u03b9\u03bf \u03bb\u03cc\u03b3\u03bf \u03c7\u03c1\u03b5\u03b9\u03b1\u03c3\u03c4\u03b5\u03af \u03ad\u03bd\u03b1 \u03c4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf \u03bd\u03b1 \u03c4\u03bf \u03ba\u03ac\u03bd\u03bf\u03c5\u03bc\u03b5 \u03b3\u03b9\u03bd\u03cc\u03bc\u03b5\u03bd\u03bf \u03b4\u03b5\u03bd \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03c0\u03b1\u03c1\u03ac \u03bd\u03b1 \u03b2\u03c1\u03bf\u03cd\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03bf\u03c5 \u03ad\u03c3\u03c4\u03c9 x1<\/sub> \u03ba\u03b1\u03b9 x2<\/sub> \u03ba\u03b1\u03b9 \u03c3\u03c4\u03b7 \u03c3\u03c5\u03bd\u03ad\u03c7\u03b5\u03b9\u03b1 \u03bd\u03b1 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ae\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf\u03bd \u03c4\u03cd\u03c0\u03bf: [su_note color=”#2ec4b6″] <\/p>\n

  <\/span>   <\/span>\"\[\alpha x^2+\beta x+\gamma=a(x-x_1)(x-x_2)\]\"<\/p>\n

[\/su_note] \u0391\u03c2 \u03b4\u03bf\u03cd\u03bc\u03b5 \u03ad\u03bd\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1:<\/p>\n

\"\u0394\u03b5\u03c5\u03c4\u03b5\u03c1\u03bf\u03b2\u03ac\u03b8\u03bc\u03b9\u03b1\u0388\u03c3\u03c4\u03c9 \u03cc\u03c4\u03b9 \u03b8\u03ad\u03bb\u03bf\u03c5\u03bc\u03b5 \u03bd\u03b1 \u03bc\u03b5\u03c4\u03b1\u03c4\u03c1\u03ad\u03c8\u03bf\u03c5\u03bc\u03b5 \u03c3\u03b5 \u03b3\u03b9\u03bd\u03cc\u03bc\u03b5\u03bd\u03bf \u03c4\u03bf \"x^2+3x-4\". \u03a0\u03c1\u03ce\u03c4\u03b1 \u03b1\u03c0’ \u03cc\u03bb\u03b1 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b2\u03c1\u03bf\u03cd\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03bb\u03cc\u03b3\u03bf \u03b1\u03c5\u03c4\u03cc \u03bb\u03cd\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b7\u03bd \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 <\/p>\n

  <\/span>   <\/span>\"\[x^2+3x-4=0\]\"<\/p>\n

. \u0388\u03c7\u03bf\u03c5\u03bc\u03b5 \"\left.\begin{matrix} \alpha=1\\ \beta=3\\ \gamma=-4\end{matrix}\right\}\" \u03ba\u03b1\u03b9 \"\Delta=\beta^2-4\alpha\gamma=3^2-4\cdot 1\cdot (-4)=9+16=25\" \u03bf\u03c0\u03cc\u03c4\u03b5 \u03bf\u03b9 \u03c1\u03af\u03b6\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \"x_1,x_2=\frac{-\beta\pm\sqrt{\Delta}}{2\alpha}=\frac{-3\pm5}{2}\Rightarrow\" \"\left\{\begin{matrix}x_1=\frac{-3-5}{2}=-4\\x_2=\frac{-3+5}{2}=1\end{matrix}\"<\/p>\n

\u03a3\u03cd\u03bc\u03c6\u03c9\u03bd\u03b1 \u03bc\u03b5 \u03b1\u03c5\u03c4\u03ac \u03c0\u03bf\u03c5 \u03b1\u03bd\u03b1\u03c6\u03ad\u03c1\u03b1\u03bc\u03b5 \u03c0\u03b9\u03bf \u03c0\u03ac\u03bd\u03c9 \u03c0\u03b1\u03c1\u03b1\u03b3\u03bf\u03bd\u03c4\u03bf\u03c0\u03bf\u03b9\u03bf\u03cd\u03bc\u03b5 \u03c4\u03bf \u03c4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf \u03bc\u03b5 \u03c4\u03bf\u03bd \u03c4\u03cd\u03c0\u03bf \u03ba\u03b1\u03b9 \u03c0\u03b1\u03af\u03c1\u03bd\u03bf\u03c5\u03bc\u03b5<\/p>\n

  <\/span>   <\/span>\"\[x^2+3x-4=1[x-(-4)](x-1)=(x+4)(x-1)\]\"<\/p>\n

\u03b8\u03b1 \u03b4\u03bf\u03cd\u03bc\u03b5 \u03ba\u03b1\u03b9 \u03b4\u03cd\u03bf \u03b1\u03ba\u03cc\u03bc\u03b7 \u03c0\u03b1\u03c1\u03b1\u03b4\u03b5\u03af\u03b3\u03bc\u03b1\u03c4\u03b1 \u03b3\u03b9\u03b1\u03c4\u03af \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03bd \u03bd\u03b1 \u03b4\u03b7\u03bc\u03b9\u03bf\u03c5\u03c1\u03b3\u03ae\u03b8\u03b7\u03ba\u03b1\u03bd \u03b1\u03c0\u03bf\u03c1\u03af\u03b5\u03c2 \u03c3\u03b5 \u03bf\u03c1\u03b9\u03c3\u03bc\u03ad\u03bd\u03bf\u03c5\u03c2 \u03b1\u03c0\u03cc \u03b5\u03c3\u03ac\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03c4\u03b9 \u03ba\u03ac\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c3\u03c4\u03b7\u03bd \u03c0\u03b5\u03c1\u03af\u03c0\u03c4\u03c9\u03c3\u03b7 \u03c0\u03bf\u03c5 \u03b4\u03b5\u03bd \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03c1\u03af\u03b6\u03b5\u03c2 \u03ae \u03c3\u03c4\u03b7\u03bd \u03c0\u03b5\u03c1\u03af\u03c0\u03c4\u03c9\u03c3\u03b7 \u03c0\u03bf\u03c5 \u03c4\u03bf \u03c4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf \u03ad\u03c7\u03b5\u03b9 \u03b4\u03b9\u03b1\u03ba\u03c1\u03af\u03bd\u03bf\u03c5\u03c3\u03b1 \u03af\u03c3\u03b7 \u03bc\u03b5 \u03bc\u03b7\u03b4\u03ad\u03bd \u0391\u03bd \u03ad\u03bd\u03b1 \u03c4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf \u03cc\u03c0\u03c9\u03c2 \u03b3\u03b9\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 \u03c4\u03bf x2<\/sup>+x+1 \u03ad\u03c7\u03b5\u03b9 \u03b4\u03b9\u03b1\u03ba\u03c1\u03af\u03bd\u03bf\u03c5\u03c3\u03b1 \u03b1\u03c1\u03bd\u03b7\u03c4\u03b9\u03ba\u03ae (\u0394=-3) \u03c4\u03cc\u03c4\u03b5 \u03cc\u03c0\u03c9\u03c2 \u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03b4\u03b5\u03bd \u03ad\u03c7\u03b5\u03b9 \u03c1\u03af\u03b6\u03b5\u03c2 \u03ba\u03b9 \u03ad\u03c4\u03c3\u03b9 \u03b4\u03b5\u03bd \u03bc\u03b5\u03c4\u03b1\u03c4\u03c1\u03ad\u03c0\u03b5\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03b3\u03b9\u03bd\u03cc\u03bc\u03b5\u03bd\u03bf.<\/p>\n

\u0395\u03bd\u03ce \u03b1\u03bd \u03bc\u03b1\u03c2 \u03b4\u03c9\u03b8\u03b5\u03af \u03b3\u03b9\u03b1 \u03c0\u03b1\u03c1\u03b1\u03b3\u03bf\u03bd\u03c4\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7 \u03ad\u03bd\u03b1 \u03c4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf \u03cc\u03c0\u03c9\u03c2 \u03c4\u03bf 4x2<\/sup>-12x+9 \u03b8\u03b1 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5>\"\left.\begin{matrix}\alpha=4\\ \beta=-12\\ \gamma=9\end{matrix}\right\}\Rightarrow\Delta=144-4\cdot4\cdot9=144-144=0\" \u03c0\u03c1\u03ac\u03b3\u03bc\u03b1 \u03c0\u03bf\u03c5 \u03c3\u03b7\u03bc\u03b1\u03af\u03bd\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03b4\u03cd\u03bf \u03c1\u03af\u03b6\u03b5\u03c2 \u03bc\u03cc\u03bd\u03bf \u03c0\u03bf\u03c5 \u03c3\u03c4\u03b7\u03bd \u03c0\u03b5\u03c1\u03af\u03c0\u03c4\u03c9\u03c3\u03b7 \u03b1\u03c5\u03c4\u03ae \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03b5\u03c2 \u03bc\u03b5\u03c4\u03b1\u03be\u03cd \u03c4\u03bf\u03c5\u03c2. \u03a0\u03c1\u03ac\u03b3\u03bc\u03b1\u03c4\u03b9 <\/p>\n

  <\/span>   <\/span>\"\[x_1=x_2=\frac{-\beta\pm 0}{2a}=\frac{12}{2\cdot4}=\frac{3}{2}\]\"<\/p>\n

\u0388\u03c4\u03c3\u03b9 \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ce\u03bd\u03c4\u03b1\u03c2 \u03c4\u03bf\u03bd \u03c4\u03cd\u03c0\u03bf \u03c0\u03bf\u03c5 \u03b4\u03ce\u03c3\u03b1\u03bc\u03b5 \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9 \u03c0\u03b1\u03af\u03c1\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b5\u03bb\u03b9\u03ba\u03ac <\/p>\n

  <\/span>   <\/span>\"\[4x^2-12x+9=4(x-\frac{3}{2})(x-\frac{3}{2})\]\"<\/p>\n

\u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03bc\u03ac\u03bb\u03bb\u03bf\u03bd \u03b8\u03b1 \u03ae\u03c4\u03b1\u03bd \u03c0\u03b9\u03bf \u03cc\u03bc\u03bf\u03c1\u03c6\u03bf \u03b1\u03bd \u03c4\u03bf \u03b3\u03c1\u03ac\u03c6\u03b1\u03bc\u03b5 \u03ad\u03c4\u03c3\u03b9 <\/p>\n

  <\/span>   <\/span>\"\[4x^2-12x+9=4(x-\frac{3}{2})(x-\frac{3}{2})\]\"<\/p>\n

  <\/span>   <\/span>\"\[4x^2-12x+9=4(x-\frac{3}{2})^2\]\"<\/p>\n

  <\/span>   <\/span>\"\[4x^2-12x+9=2^2(x-\frac{3}{2})^2\]\"<\/p>\n

  <\/span>   <\/span>\"\[4x^2-12x+9=\left\{2(x-\frac{3}{2})\right\}^2\]\"<\/p>\n

  <\/span>   <\/span>\"\[4x^2-12x+9=(2x-3)^2\]\"<\/p>\n

\u03a0\u03b1\u03c1\u03b1\u03c4\u03b7\u03c1\u03bf\u03cd\u03bc\u03b5 \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd \u03cc\u03c4\u03b9 \u03bf \u03c4\u03cd\u03c0\u03bf\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03b1\u03b3\u03bf\u03bd\u03c4\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b7 \u03c4\u03c1\u03b9\u03c9\u03bd\u03cd\u03bc\u03bf\u03c5 “\u03b4\u03bf\u03c5\u03bb\u03b5\u03cd\u03b5\u03b9” \u03ba\u03b1\u03b9 \u03cc\u03c4\u03b1\u03bd \u0394>0 (\u03b4\u03cd\u03bf \u03c1\u03af\u03b6\u03b5\u03c2 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03ad\u03c2) \u03b1\u03bb\u03bb\u03ac \u03ba\u03b1\u03b9 \u03cc\u03c4\u03b1\u03bd \u0394=0 (\u03b4\u03cd\u03bf \u03c1\u03af\u03b6\u03b5\u03c2 \u03af\u03c3\u03b5\u03c2). \u0391\u03bd \u03ba\u03b1\u03b9 \u03cc\u03c0\u03c9\u03c2 \u03b2\u03bb\u03ad\u03c0\u03bf\u03c5\u03bc\u03b5 \u03ba\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03bf \u03b1\u03ba\u03c1\u03b9\u03b2\u03ce\u03c2 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 \u03c4\u03bf\"4x^2-12x+9=(2x-3)^2\" \u03bc\u03b1\u03c2 \u03b4\u03b5\u03af\u03c7\u03bd\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03c4\u03bf \u03c4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf \u03ae\u03c4\u03b1\u03bd \u03c4\u03b1\u03c5\u03c4\u03cc\u03c4\u03b7\u03c4\u03b1 \u03b1\u03bb\u03bb\u03ac \u03b4\u03b5\u03bd \u03c4\u03bf \u03b5\u03af\u03c7\u03b1\u03bc\u03b5 \u03c0\u03c1\u03bf\u03c3\u03ad\u03be\u03b5\u03b9. \u0391\u03c5\u03c4\u03cc \u03cc\u03bc\u03c9\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ba\u03b1\u03bd\u03cc\u03bd\u03b1\u03c2 \u03c0\u03bf\u03c5 \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 \u03c0\u03ac\u03bd\u03c4\u03b1 “\u03cc\u03c4\u03b1\u03bd \u03b7 \u03b4\u03b9\u03b1\u03ba\u03c1\u03af\u03bd\u03bf\u03c5\u03c3\u03b1 \u03b5\u03bd\u03cc\u03c2 \u03c4\u03c1\u03b9\u03c9\u03bd\u03cd\u03bc\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03af\u03c3\u03b7 \u03bc\u03b5 \u03bc\u03b7\u03b4\u03ad\u03bd \u03c4\u03bf \u03c4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf \u03ad\u03c7\u03b5\u03b9 \u03b4\u03cd\u03bf \u03c1\u03af\u03b6\u03b5\u03c2 ‘\u03b9\u03c3\u03b5\u03c2 \u03c71<\/sub>=\u03c72<\/sub>“<\/strong> \u03ba\u03b9 \u03b5\u03c0\u03bf\u03bc\u03ad\u03bd\u03c9\u03c2 \u03b8\u03b1 \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 <\/p>\n

  <\/span>   <\/span>\"\[\alpha x^2+\beta x+\gamma=\alpha(x-x_1)^2\]\"<\/p>\n

\u03a3\u03c5\u03bd\u03bf\u03c8\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd \u03cc\u03bb\u03b1 \u03c4\u03b1 \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5:<\/p>\n

[su_box title=”\u039c\u03b5\u03c4\u03b1\u03c4\u03c1\u03bf\u03c0\u03ae \u03c4\u03c1\u03b9\u03c9\u03bd\u03cd\u03bc\u03bf\u03c5 \u03c3\u03b5 \u03b3\u03b9\u03bd\u03cc\u03bc\u03b5\u03bd\u03bf” color=”#2ec4b6″]<\/p>\n

\u03a4\u03bf \u03c4\u03c1\u03b9\u03ce\u03bd\u03c5\u03bc\u03bf<\/span> \"\alpha x^2+\beta x+\gamma\"<\/p>\n

[su_list style=”arrow”]<\/p>\n