Question
Download Solution PDFमान लीजिए α और β समीकरण x2 - ax - bx + ab - c = 0 के मूल हैं। वह कौन-सा द्विघाती समीकरण है जिसके मूल a और b हैं?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFप्रयुक्त सूत्र:
यदि α और β द्विघाती समीकरण ax2 + bx + c = 0 के मूल हैं।
मूल का योग α + β = -b/a
मूल का गुणनफल αβ = c/a
मूल α और β वाले समीकरणों को निम्न रूप में लिखा जा सकता है
x2 - (α + β)x + αβ = 0
गणना:
दिया गया है कि, α और β समीकरण के मूल हैं।
x2 - ax - bx + ab - c = 0
⇒ x2 - (a + b)x + (ab - c) = 0
अतः मूल का योग
α + β = a + b -----(1)
मूल का गुणनफल
αβ = ab - c
⇒ ab = αβ + c -----(2)
इसलिए, मूल a और b वाला द्विघाई समीकरण निम्न है
x2 - (a + b)x + ab = 0
समीकरण (1) और (2) से मान को रखने पर।
⇒ x2 - (α + β)x + αβ + c = 0
∴ x2 - αx - βx + α β + c = 0
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