द्विघात समीकरण ज्ञात कीजिए जिसका एक मूल  है।

  1. x2 + 10x + 5 = 0
  2. x2 - 5x + 10 = 0
  3. x2 - 10x + 5 = 0
  4. x2 + 5x - 10 = 0

Answer (Detailed Solution Below)

Option 3 : x2 - 10x + 5 = 0
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दिया गया है:

समीकरण का एक मूल  है

संकल्पना: 

यदि द्विघात समीकरण का एक मूल के स्वरुप में है तब अन्य मूल संयुग्मी  होंगे और इसके विपरीत।

द्विघात समीकरण: x2 - (मूलों का योगफल) + (मूलों का गुणनफल) = 0

गणना: 

माना α =  और β =  

मूलों का योगफल = α + β =   

मूलों का गुणनफल = α β =  = 25 - 20 = 5

अब, द्विघात समीकरण = x2 - 10x + 5 = 0 

अतः अभीष्ट द्विघात समीकरण x2 - 10x + 5 = 0 है।

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