\(2 + \sqrt 5 \) এবং \(2 - \sqrt 5\) মূলের সাথে সম্পর্কিত দ্বিঘাত সমীকরণটি কী?

  1. x 2 - 4x - 1 = 0
  2. x 2 + 4x - 1 = 0
  3. x 2 - 4x + 1 = 0
  4. x 2 + 4x + 1 = 0

Answer (Detailed Solution Below)

Option 1 : x 2 - 4x - 1 = 0
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Detailed Solution

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প্রদত্ত,

দুটি মূল হল 2 + √5 এবং 2 - √5

অনুসৃত ধারণা:

দ্বিঘাত সমীকরণটি হলো 

x2 - (মূলের সমষ্টি)x + মূলের গুণফল = 0

গণনা:

ধরা যাক,  দুটি মূল হল A এবং B 

⇒ A = 2 + √5 এবং B = 2 - √5

⇒ A + B = 2 + √5 + 2 - √5 = 4

⇒ A × B = (2 + √5)(2 - √5) = 4 - 5 = -1

তাহলে সমীকরণ হল 

∴ x 2 - 4x - 1 = 0

F1 Shailesh 17.5.21-Pallavi D2 (1)

দ্বিঘাত সমীকরণের জন্য ax2 + bx + c = 0

বর্গের যোগফল = (-b/a) = 4/1

বর্গ করে পাই  = c/a = -1/1

তাই, b = -4

সুতরাং x এর সহগটি ঋণাত্মক হবে। 

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