मूलों \(2 + \sqrt 5 \) तथा \(2 - \sqrt 5\) के संगत द्विघातीय समीकरण है

  1. x2 - 4x - 1 = 0
  2. x2 + 4x - 1 = 0
  3. x2 - 4x + 1 = 0
  4. x2 + 4x + 1 = 0

Answer (Detailed Solution Below)

Option 1 : x2 - 4x - 1 = 0
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दिया गया है:

2 + √5 और 2 - √5 दो मूल हैं

अवधारणा:: 

x2 - (मूलों का योग)x + मूलों का गुणनफल = 0

गणना

माना दो मूल A और B हैं।

⇒ A = 2 + √5 और B = 2 - √5

⇒ A + B = 2 + √5 + 2 - √5 = 4

⇒ A × B = (2 + √5)(2 - √5) = 4 - 5 = -1

तो समीकरण है,

∴ x2 - 4x - 1 = 0

F1 Shailesh 17.5.21-Pallavi D2 (1)

द्विघात समीकरण, ax2 + bx + c = 0, के लिए

मूलों का योग = (-b/a) = 4/1

मूलों का गुणनफल = c/a = -1/1

तो, b = -4

अत: x के गुणांक का चिह्न ऋणात्मक है।  

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