Question
Download Solution PDFx 2 - 4x + k = 0 సమీకరణం యొక్క మూలాలలో ఒకటి x = 3. మరొక మూలం:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFఇవ్వబడినది:
సమీకరణం x 2 - 4x + k = 0
ఉపయోగించిన కాన్సెప్ట్:
వర్గ సమీకరణం యొక్క మూలాలు సమీకరణాన్ని సంతృప్తిపరుస్తాయి, కాబట్టి ఒక మూలం యొక్క విలువను ప్రతిక్షేపించడం ద్వారా, తెలియని చరాంకాన్ని మరియు అందువల్ల మరొక మూలాన్ని కనుగొనవచ్చు.
గణనం:
సమీకరణంలో x స్థానంలో 3ని ప్రతిక్షేపించగా,
కాబట్టి,
x 2 – 4x + k = 0
⇒ 9 – 12 + k = 0
⇒ k = 3
సమీకరణంలో k విలువను ప్రతిక్షేపించగా:
x 2 – 4x + 3 = 0
⇒ x 2 – 3x – x + 3 = 0
⇒ x(x – 3) – 1(x – 3) = 0
⇒ (x – 3)(x – 1) = 0
⇒ x = 3 మరియు 1
∴ సమీకరణం యొక్క ఇతర మూలం 1.
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