ext/static/chunks/a3334c652b046c3c.js","/_next/static/chunks/81b954b7224a589b.js","/_next/static/chunks/5a05ab8ee13b0bc4.js","/_next/static/chunks/6a6cb77c3f1aa625.js","/_next/static/chunks/32fdb7a303638b44.js","/_next/static/chunks/3be0177d875a105f.js","/_next/static/chunks/03e5fc0c4e7453d7.js","/_next/static/chunks/5c76b79364f9765a.js","/_next/static/chunks/718b487edc6243e6.js","/_next/static/chunks/f4c85fceb03175a8.js","/_next/static/chunks/1d422ca4614fbd39.js","/_next/static/chunks/84af6b765e7bcd95.js","/_next/static/chunks/91c05db7234c690f.js"],""] 20:I[605500,["/_next/static/chunks/18e2520e95b8024c.js","/_next/static/chunks/09dfb6945efb942a.js","/_next/static/chunks/c87c7a10fa5002a5.js","/_next/static/chunks/62b540b0ec1fd623.js","/_next/static/chunks/397198a845d2c3dc.js","/_next/static/chunks/99745078d480a4ae.js","/_next/static/chunks/fdc5802a61eabbac.js","/_next/static/chunks/7bebe4ee53854e8e.js","/_next/static/chunks/a3334c652b046c3c.js","/_next/static/chunks/81b954b7224a589b.js","/_next/static/chunks/5a05ab8ee13b0bc4.js","/_next/static/chunks/6a6cb77c3f1aa625.js","/_next/static/chunks/32fdb7a303638b44.js","/_next/static/chunks/3be0177d875a105f.js","/_next/static/chunks/03e5fc0c4e7453d7.js","/_next/static/chunks/5c76b79364f9765a.js","/_next/static/chunks/718b487edc6243e6.js","/_next/static/chunks/f4c85fceb03175a8.js","/_next/static/chunks/1d422ca4614fbd39.js","/_next/static/chunks/84af6b765e7bcd95.js","/_next/static/chunks/91c05db7234c690f.js"],"Image"] 21:I[909631,["/_next/static/chunks/18e2520e95b8024c.js","/_next/static/chunks/09dfb6945efb942a.js","/_next/static/chunks/c87c7a10fa5002a5.js","/_next/static/chunks/62b540b0ec1fd623.js","/_next/static/chunks/397198a845d2c3dc.js","/_next/static/chunks/99745078d480a4ae.js","/_next/static/chunks/fdc5802a61eabbac.js","/_next/static/chunks/7bebe4ee53854e8e.js","/_next/static/chunks/a3334c652b046c3c.js","/_next/static/chunks/81b954b7224a589b.js","/_next/static/chunks/5a05ab8ee13b0bc4.js","/_next/static/chunks/6a6cb77c3f1aa625.js","/_next/static/chunks/32fdb7a303638b44.js","/_next/static/chunks/3be0177d875a105f.js","/_next/static/chunks/03e5fc0c4e7453d7.js","/_next/static/chunks/5c76b79364f9765a.js","/_next/static/chunks/718b487edc6243e6.js","/_next/static/chunks/f4c85fceb03175a8.js","/_next/static/chunks/1d422ca4614fbd39.js","/_next/static/chunks/84af6b765e7bcd95.js","/_next/static/chunks/91c05db7234c690f.js"],"QuestionCard"] 22:T66d,প্রদত্ত ত্রিঘাত সমীকরণটি হল:

\( x^{3}-5 x^{2}+11 x-7=0 \)

।
যদি একটি মূল \( 2+i3 \) হয়, তাহলে বাস্তব সহগযুক্ত সমীকরণের ধর্ম অনুযায়ী, এর অনুবন্ধী মূল \( 2-i3 \) ও একটি মূল হবে।

ধরি, মূল দুটি \( \alpha = 2+i3 \) এবং \( \beta = 2-i3 \) ।

মূল দুইটির যোগফল:

\( \alpha+\beta = (2+i3) + (2-i3) = 4 \)

মূল দুইটির গুণফল:

\( \alpha\beta = (2+i3)(2-i3) = 2^2 - (i3)^2 = 4 - (-9) = 4+9=13 \)

এখন, ধরি সমীকরণটির বাস্তব মূলটি \( \gamma \)।

একটি ত্রিঘাত সমীকরণ \( x^3+ax^2+bx+c=0 \) এর মূল তিনটির যোগফল হয় \( -a \)।
আমাদের প্রদত্ত সমীকরণটি \( x^{3}-5 x^{2}+11 x-7=0 \) এর জন্য, মূল তিনটির যোগফল হবে: \( -(-5) = 5 \) ।

সুতরাং, \( \alpha + \beta + \gamma = 5 \)
যেহেতু আমরা জানি \( \alpha + \beta = 4 \), তাহলে:

\( 4 + \gamma = 5 \)

\( \gamma = 5 - 4 \)

\( \gamma = 1 \)

অতএব, সমীকরণটির বাস্তব মূলটি হল 1।

( x^ 3 -5 x^ 2 +11 x-7 ) = 0 একটি ত্রিঘাত সমীকরণ। সমীকরণটির একটি মূল (2+i3 ) হলে উহার বাস্তব মূলটি কত?