Question
Download Solution PDFद्विघात समीकरण x2 − 4x + k = 0 का एक मूल x = 3 है। दूसरा मूल ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया 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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