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Let Z₁ and Z₂ be two roots of the equation x^2+a Z+b=0 being complex. Further, assume that the origin, Z₁ and Z ₂ form an equilateral triangle. Then

Options

  1. Aa^2=4 b
  2. Ba^2=b
  3. Ca^2=2 b
  4. Da^2=3 b

Correct answer

D. a^2=3 b

Step-by-step solution

z ^2+ az + b =0 ; z ₁+ z ₂=- a & z ₁ z ₂= b 0, z , z ₂ form an equilateral 0^2+ z ₁ ^2+ z ₂ ^2=0 . z ₁+ z ₁ z ₂+ z ₂ 0 (for equation , z ₁ ^2+ z ₂ ^2+ z ₃ ^2= z ₁ z ₂+ z ₂ z ₃+ z ₃ z ₁ ) z₁^2+z₂^2=z₁ z₂ or (z₁+z₂ )^2=3 z₁ z₂ a ^2=3 ~b .

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