Question
Download Solution PDFयदि a और b, x2 - x - 12 = 0 के मूल हैं और a > b है, तो x के पदों में द्विघात समीकरण क्या होगा जिसके मूल (2a - 1) और (2b + 1) हैं?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
समीकरण x2 - x - 12 = 0 के मूल a और b हैं।
दिए गए मूल: (2a - 1) और (2b + 1)
प्रयुक्त अवधारणा:
समीकरण ax2 + bx + c = 0 में,
मूलों का योग =
मूलों का गुणनफल =
मूलों का अंतर =
गणना:
समीकरण x2 - x - 12 = 0 से हम पाते हैं
नीचे दिए गए समीकरणों में इस मान को प्रतिस्थापित करना:
दिए गए मूल: (2a - 1) और (2b + 1)
इस प्रकार, गठित द्विघात समीकरण होगा:
x2 - (मूलों का योग) x + मूलों का गुणनफल = 0
⇒ x2 - 2x + (-35) = 0
⇒ x2 - 2x - 35 = 0
इसलिए, वह द्विघात समीकरण जिसके मूल (2a - 1) और (2b + 1) हैं, x2 - 2x - 35 = 0 है।
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