द्विघात समीकरण x2 − 4x + k = 0 का एक मूल x = 3 है। दूसरा मूल ज्ञात कीजिए।

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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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दिया गया है:

समीकरण: x2 − 4x + k = 0

प्रयुक्त अवधारणा:

एक द्विघात समीकरण के मूल समीकरण को संतुष्ट करते हैं, इसलिए एक मूल का मान रखकर एक अज्ञात चर और दूसरा मूल ज्ञात किया जा सकता है।

गणना:

समीकरण में x का मान = 3 रखते हैं। 

इसलिए,

x2 – 4x + k = 0

⇒ 9 – 12 + k = 0

⇒ k = 3

k का मान समीकरण में रखने पर, हमें प्राप्त होता है:

x2 – 4x + 3 = 0

⇒ x2 – 3x – x + 3 = 0

⇒ x(x – 3) – 1(x – 3) = 0

⇒ (x – 3)(x – 1) = 0

⇒ x = 3 और 1 

∴ समीकरण का दूसरा मूल 1 है।

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