যদি ω একের ঘনমূল হয়, তাহলে নীচের সমীকরণের একটি মূল কত? 

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  1. x = ω
  2. x = 0
  3. x = 1
  4. x = ω2

Answer (Detailed Solution Below)

Option 2 : x = 0

Detailed Solution

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ধারণা:

ω যদি একের ঘনমূল হয়, অর্থাৎ ω3 = 1

তাহলে 1 + ω + ω2 = 0

ω4 = ω3ω = ω [∵ ω3 =1]

গণনা:

প্রদত্ত:

C'1 = C1 + C2

R'2 = R2 - R1 এবং R'3 = R3 - R1

প্রথম স্তম্ভকে প্রসারিত করে:

∴ x[(x + ω2 - ω)(x + ω - ω2) - (1 - ω)(1 - ω2)]

∴ x[x2 + ωx - ω2x + ω2x + ω3 - ω4 - ωx - ω2 + ω3 - 1 + ω2 + ω - ω3]

∴ x3 = 0 (∵ ω3 = 1 এবং ω4 = ω 3 ω ⇒ ω)

∴ x = 0

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