Question
Download Solution PDFमूलों \(2 + \sqrt 5 \) तथा \(2 - \sqrt 5\) के संगत द्विघातीय समीकरण है
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया 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
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।
Last updated on Jun 2, 2025
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