x2 - 4x + k = 0 சமன்பாட்டின் மூலங்களில் ஒன்று x = 3 ஆகும். மற்ற மூலம்:

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RRB ALP CBT I 14 Aug 2018 Shift 1 Official Paper
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  1. x = −1
  2. x = −4
  3. x = 4
  4. x = 1

Answer (Detailed Solution Below)

Option 4 : x = 1
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கொடுக்கப்பட்டவை:
 
சமன்பாடு x2 - 4x + k = 0
 
பயன்படுத்தப்பட்ட கருத்து:
 
இருபடிச் சமன்பாட்டின் மூலங்கள் சமன்பாட்டை நிறைவு செய்கின்றன, எனவே ஒரு மூலத்தின் மதிப்பை வைப்பதன் மூலம், அறியப்படாத மாறியையும் அதனால் மற்ற மூலத்தையும் காணலாம்.
 
கணக்கீடு:
 
சமன்பாட்டில் x ஐ 3 ஐ வைப்போம்
 
அதனால்,

x2 – 4x + k = 0

⇒ 9 – 12 + k = 0

⇒ k = 3

சமன்பாட்டில் k இன் மதிப்பை இட, நாம் பெறுவது:

x2 – 4x + 3 = 0

⇒ x2 – 3x – x + 3 = 0

⇒ x(x – 3) – 1(x – 3) = 0

⇒ (x – 3)(x – 1) = 0

⇒ x = 3 மற்றும் 1 

சமன்பாட்டின் மற்ற மூலம் 1 ஆகும்.

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