Question
Download Solution PDFयदि समीकरण 2x2 - 3x - 5 = 0 के मूल α और β हैं, तब निम्नलिखित में से किस समीकरण के मूल \(\frac{\alpha}{\beta}\) और \(\frac{\beta}{\alpha}\) हैं?
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समीकरण 2x 2 - 3x - 5 = 0 के मूल α और β हैं।
एक अन्य समीकरण के मूल \(\frac{\alpha}{\beta}\) और \(\frac{\beta}{\alpha}\) हैं।
गणना:
दिए गए समीकरण पर हिट और ट्रायल विधि का उपयोग करके α और β के मान ज्ञात करें।
2x 2 - 3x - 5 = 0
= 2x 2 - 5x + 2x - 5
= x(2x - 5) +1(2x - 5)
= (2x - 5)(x + 1)
x = \(\frac{5}{2}\) और x = -1
इस प्रकार α = \(\frac{5}{2}\) और β = -1
अब \(\frac{\alpha}{\beta}\) और \(\frac{\beta}{\alpha}\) को हल करने पर, हमें प्राप्त होता है
\(\frac{\alpha}{\beta}\) = \(\frac{-5}{2}\)
\(\frac{\beta}{\alpha}\) = \(\frac{-2}{5}\)
अब,
द्विघात समीकरण जिसके मूल \(\frac{\alpha}{\beta}\) और \(\frac{\beta}{\alpha}\) हैं:
(x - (\(\frac{-5}{2}\))) (x - (\(\frac{-2}{5}\))) = 0
⇒ (x + 5/2) (x + 2/5) = 0
⇒ x2 + 5x/2 + 2x/5 + 1 = 0
⇒ (10x2 + 25x + 4x + 10)/10 = 0
⇒ 10x2 + 29x + 10 = 0
∴ सही उत्तर विकल्प (2) हैLast updated on Jul 18, 2025
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