Question
Download Solution PDFनिम्नलिखित में से कौन सा द्विघात समीकरण 4x2 - 7√3x + 12 = 0 के मूलों की प्रकृति को वर्णित करता है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया है:
4x2 - 7√3x + 12 = 0
प्रयुक्त सूत्र और अवधारणा:
द्विघात समीकरण के मूल ज्ञात करने के लिए, हमें विविक्तकर (D) ज्ञात करने की आवश्यकता है।
समीकरण \(ax^2+bx+c=0\) के लिए:
\(D=b^2-4ac\)
यदि D > 0, समीकरण के 2 वास्तविक और भिन्न मूल हैं।
यदि D < 0, समीकरण के 2 सम्मिश्र मूल हैं (अर्थात् कोई वास्तविक मूल नहीं है)।
यदि D = 0, समीकरण का केवल 1 वास्तविक मूल है (या 2 समान मूल)।
गणना:
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
\(D=b^2-4ac\)
\(ax^2+bx+c=0\)
चूंकि D = - 45, यानी < 0, समीकरण के 2 भिन्न सम्मिश्र मूल होंगे।
इसलिए, द्विघात समीकरण '4x2 - 7√3x + 12 = 0' का कोई वास्तविक मूल नहीं है।
Last updated on Jun 30, 2025
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