Page 85 - math 12

ﱢﻱﺮﻔﺼﻟﺍ ِﺏﺮﻀﻟﺍ ِﺔﻴﺻﺎﺧ ﻝﺎﻤﻌﺘﺳﺎﺑ ِﺕﻻﺩﺎﻌﻤﻟﺍ ﻞﺣ [4-3-2]
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Solving the Equations by Using Zero Product Property

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ﻦﻳﺩﺪﻌﻟﺍ ﺪﺣﺃ ﻥﻮﻜﻳ ﻥﺃ ﺐﺠﻳ ﻪﻧﺈﻓ ًﺍﺮﻔﺻ ﻱﻭﺎﺴﻳ ﻦﻳﺩﺪﻋ ِﺏﺮﺿ ﺔﺠﻴﺘﻧ ﻥﺎﻛ ﺍﺫﺇ :ﱢﻱﺮﻔﺼﻟﺍ ِﺏﺮﻀﻟﺍ ﺔﻴﺻﺎﺧ
. b=0 ﻭﺃ a=0 ﻰﻟﺍ ﻱﺩﺆﻳ ab = 0 ﻥﺎﻛ ﺍﺫﺇ ﻪﻧﺈﻓ ﺍﺬﻟﻭ ، 0×8 = 0 ، 5×0 =0 ُﻼﺜﻣ ،ًﺍﺮﻔﺻ ﻱﻭﺎﺴﻳ

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ﺭﺎﺘﻣﻷﺎﺑ ﻢﻬﺳ ﻉﺎﻔﺗﺭﺃ L= -5t + 30t ُﻥﻮﻧﺎﻘﻟﺍ ﻞﺜﻤﻳ :ﺔﺿﺎﻳﺭ (3) ﻝﺎﺜﻣ
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ِﺐﺴﺣﺍ .ﻲﻧﺍﻮﺜﻟﺎﺑ ﻦﻣﺰﻟﺍ t ﻞﺜﻤﺗ ﺫﺇ ءﺍﻮﻬﻟﺍ ﻲﻓ ﺭﺎﺘﺨﻣ ﻪﻘﻠﻁﺃ ﻱﺬﻟﺍ
.ﻪﻨﻣ ﻖﻠﻄﻧﺍ ﻱﺬﻟﺍ ﻉﺎﻔﺗﺭﻻﺍ ﻦﻣ ﻢﻬﺴﻟﺍ ُﺩﻮﻌﻳ ﻲﻜﻟ ﻡﺯﻼﻟﺍ َﻦﻣﺰﻟﺍ
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L = 0 ﻥﻮﻜﻳ ﺎﻣﺪﻨﻋ ،ﻪﻨﻣ ﻖﻠﻄﻧﺍ ﻱﺬﻟﺍ ﻉﺎﻔﺗﺭﻻﺍ ﺪﻨﻋ ﻢﻬﺴﻟﺍ ﻥﻮﻜﻳ

-5t + 30t = 0 ﺍﺬﻟ
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5t (-t + 6) = 0 ﻙﺮﺘﺸﻤﻟﺍ ﻞﻣﺎﻌﻟﺍ ﺝﺍﺮﺨﺘﺳﺎﺑ ﻞﻠﺤﻧ
ﻱﺮﻔﺼﻟﺍ ﺏﺮﻀﻟﺍ ﺔﻴﺻﺎﺧ
5t = 0 ⇒ t = 0
ﻭﺃ
-t +6 = 0 ⇒ t = 6

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.ﻲﻧﺍﻮﺜﻟﺎﺑ ﻢﻬﺴﻟﺍ ﻕﻼﻄﻧﺍ ُﻦﻣﺯ ﻮﻫ t = 0
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. ﻲﻧﺍﻮﺜﻟﺎﺑ ﻪﻨﻣ ﻖﻠﻄﻧﺍ ﻱﺬﻟﺍ ﻉﺎﻔﺗﺭﻻﺍ ﻰﻟﺍ ِﺓﺩﻮﻌﻠﻟ ﻢﻬﺴﻟﺍ ﻪﻗﺮﻐﺘﺳﺍ ﻱﺬﻟﺍ ُﻦﻣﺰﻟﺍ ﻮﻫ t = 6
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:ﱢﻱﺮﻔﺼﻟﺍ ِﺏﺮﻀﻟﺍ ِﺔﻴﺻﺎﺧ ﻝﺎﻤﻌﺘﺳﺎﺑ ﺔﻴﻟﺎﺘﻟﺍ ِﺕﻻﺩﺎﻌﻤﻟﺍ ﻞﺣ (4) ﻝﺎﺜﻣ
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i) ( x - 3) ( x + 5 ) = 0 ⇒ x - 3 = 0 ﻭﺃ x+ 5 = 0 ⇒ x = 3 ﻭﺃ x = - 5

ii) ( t + 8) ( t + 8 ) = 0 ⇒ t + 8 = 0 ﻭﺃ t+ 8 = 0 ⇒ t = -8 ﻭﺃ t = - 8 ⇒ t = -8

iii) ( y - 12) ( y – 9) = 0 ⇒ y - 12 = 0 ﻭﺃ y - 9 = 0 ⇒ y = 12 ﻭﺃ y = 9

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iv) ( 2z - 7) ( z + 3 ) = 0 ⇒ 2z - 7 = 0 ﻭﺃ z + 3= 0 ⇒ z = ﻭﺃ z = - 3
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v) ( n + 3 ) ( n - 2 ) = 0 ⇒ n + 3 = 0 ﻭﺃ n - 2 = 0 ⇒ n = - 3 ﻭﺃ n = 2

vi) x - x = 0 ⇒ x ( x - 1) = 0 ⇒ x = 0 ﻭﺃ x - 1 = 0 ⇒ x = 0 ﻭﺃ x = 1
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vii) 4y - 16y = 0 ⇒ 4y( y - 4) = 0 ⇒ 4y = 0 ﻭﺃ y - 4 = 0 ⇒ y = 0 ﻭﺃ y = 4

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viii) 5z - 5z = 0 ⇒ 5z( 1 - z) = 0 ⇒ 5z = 0 ﻭﺃ 1 - z = 0 ⇒ z = 0 ﻭﺃ z = 1

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ix) 12 h + 2 h = 0 ⇒ 2 3 h + 2 h = 0 ⇒ 2h ( 3 h + 1) = 0

⇒ 2h = 0 ﻭﺃ 3 h +1 = 0 ⇒ h = 0 ﻭﺃ h = - 1
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