ºÝºÝߣ

ºÝºÝߣShare a Scribd company logo
§°§â§ç§à§ß §è§à§Ô§è§à§Ý§Ò§à§â §ã§å§â§Ô§å§å§Ý§î - §¢§à§Ý§à§â§ã§Ñ§Û§ç§Ñ§ß §Ò§Ñ§Ô§ê
? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß 2 §ê§Ú§Û§Õ
§ä§ï§ß§è?? §Ò§à§Ý m §ä§à§à§Ô §à§Ý.
? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý §Ò§à§Õ§Ú§ä §ñ§Ù§Ô§å§å§â§Ô?§Û
§Ò§Ñ§Û§ç m §ä§à§à§Ô §à§Ý.
? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß §ñ§Ù§Ô§å§å§â§å§å§Õ §ß§î (-2,2)
§Ù§Ñ§Ó§ã§Ñ§â§ä §à§â§ê§Ú§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý.
? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß §Ò?§ç §ñ§Ù§Ô§å§å§â §ß§î
0,5§Ñ§Ñ§ã §Ú§ç §Ò§Ñ§Û§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý.
? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý 2§à§à§ã §Ò§Ñ§Ô§Ñ
§ñ§Ý§Ô§Ñ§Ñ§ä§Ñ§Û 2 §ê§Ú§Û§Õ§ä§ï§Û §Ò§Ñ§Û§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç
§å§ä§Ô§í§Ô §à§Ý.
? -§Ú§Û§ß §ç§å§Ó§î§Õ §ä§ï§ß§è§ï§ä§Ô§ï§Ý
§Ò§Ú§ê ?§ß§ï§ß §Ò§Ñ§Û§ç m §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý.
§°§â§ç§à§ß §è§à§Ô§è§à§Ý§Ò§à§â §ã§å§â§Ô§å§å§Ý§î - §¢§à§Ý§à§â§ã§Ñ§Û§ç§Ñ§ß §Ò§Ñ§Ô§ê
§°§â§ç§à§ß §è§à§Ô§è§à§Ý§Ò§à§â §ã§å§â§Ô§å§å§Ý§î - §¢§à§Ý§à§â§ã§Ñ§Û§ç§Ñ§ß §Ò§Ñ§Ô§ê
§°§â§ç§à§ß §è§à§Ô§è§à§Ý§Ò§à§â §ã§å§â§Ô§å§å§Ý§î - §¢§à§Ý§à§â§ã§Ñ§Û§ç§Ñ§ß §Ò§Ñ§Ô§ê
§°§â§ç§à§ß §è§à§Ô§è§à§Ý§Ò§à§â §ã§å§â§Ô§å§å§Ý§î - §¢§à§Ý§à§â§ã§Ñ§Û§ç§Ñ§ß §Ò§Ñ§Ô§ê
§°§â§ç§à§ß §è§à§Ô§è§à§Ý§Ò§à§â §ã§å§â§Ô§å§å§Ý§î - §¢§à§Ý§à§â§ã§Ñ§Û§ç§Ñ§ß §Ò§Ñ§Ô§ê
? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß 2 §ê§Ú§Û§Õ §ä§ï§ß§è?? §Ò§à§Ý
§ä§à§à§Ô §à§Ý.
? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý §Ò§à§Õ§Ú§ä §ê§Ú§Û§Õ§Ô?§Û §Ò§Ñ§Û§ç §ä§à§à§Ô §à§Ý.
? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß §ê§Ú§Û§Õ??§Õ §ß§î (-2,2) §Ù§Ñ§Ó§ã§Ñ§â§ä
§à§â§ê§Ú§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý.
? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß §Ò?§ç §ê§Ú§Û§Õ §ß§î 0,5§Ñ§Ñ§ã §Ú§ç
§Ò§Ñ§Û§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý.
? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý 2-§à§à§ã §Ò§Ñ§Ô§Ñ §ñ§Ý§Ô§Ñ§Ñ§ä§Ñ§Û 2
§ê§Ú§Û§Õ§ä§ï§Û §Ò§Ñ§Û§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý.
? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß §ß§ï§Ô §ê§Ú§Û§Õ 2-§à§à§ã
§Ò§Ñ§Ô§Ñ, §ß?§Ô?? §ê§Ú§Û§Õ 3-§Ñ§Ñ§ã §Ú§ç §Ò§Ñ§Û§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô
§à§Ý.
? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß §ê§Ú§Û§Õ??§Õ§Ú§Û§ß §ç§à§à§â§à§ß§Õ
1 §Ô§ï§ã§ï§ß §ä§à§à §à§â§ê§Ú§Ø §Ò§Ñ§Û§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý.
? -§Ú§Û§ß §ç§å§Ó§î§Õ §ä§ï§ß§è§ï§ä§Ô§ï§Ý §Ò§Ú§ê
?§ß§ï§ß §Ò§Ñ§Û§ç §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý.
§°§â§ç§à§ß §è§à§Ô§è§à§Ý§Ò§à§â §ã§å§â§Ô§å§å§Ý§î - §¢§à§Ý§à§â§ã§Ñ§Û§ç§Ñ§ß §Ò§Ñ§Ô§ê
?x2+px+q=(x-x1)(x-x2)
? x1+x2=-p
? x1x2=q
? x1
2 +x2
2 = (x1+x2)2-2x1x2 = p2-2q
? x1
3 +x2
3 =(x1+x2)(x1
2 +x2
2 -x1x2) = -p(p2-3q)
? x1
4 +x2
4 = (x1
2 +x2
2 )2-2 x1
2 x2
2 = p4-4p2q+2q2
? x1
5+x2
5 =(x1
2+x2
2)(x1
3+x2
3)-x1
2x2
2 (x1+x2) =
(p2-2q)(3qp-p3)+pq2
?x3+px2+qx+r=0
? x1+x2+x3=-p
? x1x2+x1x3+x2x3=q
? x1x2x3=-r
?x1
2+x2
2+x3
2 = p2-2q
?x1
3+x2
3+x3
3 =-p3+3pq-3r
?x1
4+x2
4+x3
4 =p4-4p2q+4pr+rq2
? §¥§Ñ§â§Ñ§Ñ§ç §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß §ã§Ú§ã§ä§Ö§Þ??§Õ§Ú§Û§Ô §Ò§à§Õ.
§°§â§ç§à§ß §è§à§Ô§è§à§Ý§Ò§à§â §ã§å§â§Ô§å§å§Ý§î - §¢§à§Ý§à§â§ã§Ñ§Û§ç§Ñ§ß §Ò§Ñ§Ô§ê
? §ä§à§à§ß§í §ç§å§Ó§î§Õ
§Ò§à§Ý§à§ç§í§Ô §Ò§Ñ§ä§Ñ§Ý§Ø §ä§ï§ß§è§ï§Ý§Õ§ï§ï §ç?§â§ï§ç §ß?§ç§è§Ý§Ú§Û§Ô
§ä§à§Ô§ä§à§à.
? §æ§å§ß§Ü§è§Ú§Û§ß §ç§Ñ§Þ§Ô§Ú§Û§ß
§Ò§Ñ§Ô§Ñ §å§ä§Ô§í§Ô §à§Õ.
? - §ß§î §ã§Ú§ã§ä§Ö§Þ§Ú§Û§ß §ê§Ú§Û§Õ
§Ò§à§Ý
§Ú§Ý§ï§â§ç§Ú§Û§Ý§Ý§Ú§Û§ß
§å§ä§Ô§í§Ô §à§Ý.
? ;
§Ò§Ñ§ä§Ñ§Ý
? §ã§Ú§ã§ä§Ö§Þ§Ú§Û§Ô §Ò§à§Õ.
? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý §Ò§à§Õ.
? §ã§Ú§ã§ä§Ö§Þ§Ú§Û§Ô §Ò§à§Õ.
§°§â§ç§à§ß §è§à§Ô§è§à§Ý§Ò§à§â §ã§å§â§Ô§å§å§Ý§î - §¢§à§Ý§à§â§ã§Ñ§Û§ç§Ñ§ß §Ò§Ñ§Ô§ê

More Related Content

§°§â§ç§à§ß §è§à§Ô§è§à§Ý§Ò§à§â §ã§å§â§Ô§å§å§Ý§î - §¢§à§Ý§à§â§ã§Ñ§Û§ç§Ñ§ß §Ò§Ñ§Ô§ê

  • 2. ? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß 2 §ê§Ú§Û§Õ §ä§ï§ß§è?? §Ò§à§Ý m §ä§à§à§Ô §à§Ý. ? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý §Ò§à§Õ§Ú§ä §ñ§Ù§Ô§å§å§â§Ô?§Û §Ò§Ñ§Û§ç m §ä§à§à§Ô §à§Ý. ? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß §ñ§Ù§Ô§å§å§â§å§å§Õ §ß§î (-2,2) §Ù§Ñ§Ó§ã§Ñ§â§ä §à§â§ê§Ú§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý. ? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß §Ò?§ç §ñ§Ù§Ô§å§å§â §ß§î 0,5§Ñ§Ñ§ã §Ú§ç §Ò§Ñ§Û§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý. ? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý 2§à§à§ã §Ò§Ñ§Ô§Ñ §ñ§Ý§Ô§Ñ§Ñ§ä§Ñ§Û 2 §ê§Ú§Û§Õ§ä§ï§Û §Ò§Ñ§Û§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý. ? -§Ú§Û§ß §ç§å§Ó§î§Õ §ä§ï§ß§è§ï§ä§Ô§ï§Ý §Ò§Ú§ê ?§ß§ï§ß §Ò§Ñ§Û§ç m §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý.
  • 8. ? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß 2 §ê§Ú§Û§Õ §ä§ï§ß§è?? §Ò§à§Ý §ä§à§à§Ô §à§Ý. ? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý §Ò§à§Õ§Ú§ä §ê§Ú§Û§Õ§Ô?§Û §Ò§Ñ§Û§ç §ä§à§à§Ô §à§Ý. ? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß §ê§Ú§Û§Õ??§Õ §ß§î (-2,2) §Ù§Ñ§Ó§ã§Ñ§â§ä §à§â§ê§Ú§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý. ? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß §Ò?§ç §ê§Ú§Û§Õ §ß§î 0,5§Ñ§Ñ§ã §Ú§ç §Ò§Ñ§Û§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý. ? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý 2-§à§à§ã §Ò§Ñ§Ô§Ñ §ñ§Ý§Ô§Ñ§Ñ§ä§Ñ§Û 2 §ê§Ú§Û§Õ§ä§ï§Û §Ò§Ñ§Û§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý. ? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß §ß§ï§Ô §ê§Ú§Û§Õ 2-§à§à§ã §Ò§Ñ§Ô§Ñ, §ß?§Ô?? §ê§Ú§Û§Õ 3-§Ñ§Ñ§ã §Ú§ç §Ò§Ñ§Û§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý. ? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß §ê§Ú§Û§Õ??§Õ§Ú§Û§ß §ç§à§à§â§à§ß§Õ 1 §Ô§ï§ã§ï§ß §ä§à§à §à§â§ê§Ú§Ø §Ò§Ñ§Û§ç §Ñ §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý. ? -§Ú§Û§ß §ç§å§Ó§î§Õ §ä§ï§ß§è§ï§ä§Ô§ï§Ý §Ò§Ú§ê ?§ß§ï§ß §Ò§Ñ§Û§ç §á§Ñ§â§Ñ§Þ§Ö§ä§â§Ú§Û§ß §Ò?§ç §å§ä§Ô§í§Ô §à§Ý.
  • 10. ?x2+px+q=(x-x1)(x-x2) ? x1+x2=-p ? x1x2=q ? x1 2 +x2 2 = (x1+x2)2-2x1x2 = p2-2q ? x1 3 +x2 3 =(x1+x2)(x1 2 +x2 2 -x1x2) = -p(p2-3q) ? x1 4 +x2 4 = (x1 2 +x2 2 )2-2 x1 2 x2 2 = p4-4p2q+2q2 ? x1 5+x2 5 =(x1 2+x2 2)(x1 3+x2 3)-x1 2x2 2 (x1+x2) = (p2-2q)(3qp-p3)+pq2
  • 11. ?x3+px2+qx+r=0 ? x1+x2+x3=-p ? x1x2+x1x3+x2x3=q ? x1x2x3=-r ?x1 2+x2 2+x3 2 = p2-2q ?x1 3+x2 3+x3 3 =-p3+3pq-3r ?x1 4+x2 4+x3 4 =p4-4p2q+4pr+rq2
  • 12. ? §¥§Ñ§â§Ñ§Ñ§ç §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý§Ú§Û§ß §ã§Ú§ã§ä§Ö§Þ??§Õ§Ú§Û§Ô §Ò§à§Õ.
  • 14. ? §ä§à§à§ß§í §ç§å§Ó§î§Õ §Ò§à§Ý§à§ç§í§Ô §Ò§Ñ§ä§Ñ§Ý§Ø §ä§ï§ß§è§ï§Ý§Õ§ï§ï §ç?§â§ï§ç §ß?§ç§è§Ý§Ú§Û§Ô §ä§à§Ô§ä§à§à. ? §æ§å§ß§Ü§è§Ú§Û§ß §ç§Ñ§Þ§Ô§Ú§Û§ß §Ò§Ñ§Ô§Ñ §å§ä§Ô§í§Ô §à§Õ. ? - §ß§î §ã§Ú§ã§ä§Ö§Þ§Ú§Û§ß §ê§Ú§Û§Õ §Ò§à§Ý §Ú§Ý§ï§â§ç§Ú§Û§Ý§Ý§Ú§Û§ß §å§ä§Ô§í§Ô §à§Ý.
  • 15. ? ; §Ò§Ñ§ä§Ñ§Ý ? §ã§Ú§ã§ä§Ö§Þ§Ú§Û§Ô §Ò§à§Õ. ? §ä§ï§Ô§ê§Ú§ä§Ô§ï§Ý §Ò§à§Õ. ? §ã§Ú§ã§ä§Ö§Þ§Ú§Û§Ô §Ò§à§Õ.