Question
Download Solution PDFx2 − 4x + k = 0 या समीकरणाच्या मुळांपैकी एक x = 3 आहे.तर दुसरे मूळ काय आहे?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेले आहे:
समीकरण x2 − 4x + k = 0
वापरलेली संकल्पना:
चतुर्भुज समीकरणाची मुळे समीकरणाचे समाधान करतात, म्हणून एका रूटचे मूल्य टाकून, एक अज्ञात चल शोधू शकतो आणि म्हणून दुसरे मूळ होय.
गणना:
समीकरणात x 3 असू द्या
तर,
x2 – 4x + k = 0
⇒ 9 – 12 + k = 0
⇒ k = 3
समीकरणात k चे मूल्य टाकल्यास आपल्याला मिळते:
x2 – 4x + 3 = 0
⇒ x2 – 3x – x + 3 = 0
⇒ x(x – 3) – 1(x – 3) = 0
⇒ (x – 3)(x – 1) = 0
⇒ x = 3 आणि 1
∴ समीकरणाचे दुसरे मूळ 1 आहे.
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