समीकरण (x - 1)² + (x - 3)² + (x - 5)² = 0 के वास्तविक मूलों की संख्या क्या है?

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. कोई नहीं
  2. केवल एक
  3. केवल दो
  4. तीन

Answer (Detailed Solution Below)

Option 1 : कोई नहीं
Free
NDA 01/2025: English Subject Test
30 Qs. 120 Marks 30 Mins

Detailed Solution

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व्याख्या:

दिया गया है:

(x - 1)2 + (x - 3)2 + (x - 5)2 = 0

⇒ x² - 2x + 1 + x² - 6x + 9 + x² - 10x + 25 = 0

⇒ 3x² - 18x + 35 = 0

अब, विविक्तकर D = (-18)² - 4 x 3 x 35

= -96 < 0

इस प्रकार, दिए गए समीकरण का कोई वास्तविक मूल नहीं है।

∴ विकल्प (a) सही है

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