If the origin and roots of the equation z2+2z+q=0 form an equilateral triangle, then the value of q equals
A
34
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B
43
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C
−34
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D
−43
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Solution
The correct option is D43 Let a and b be the roots of the equation z2+2z+q=0 ∴a,b=−1±i√q−1 Since Origin, a & b form an equilateral triangle. Therefore |a|=|b|=|a−b| |a|=|b|=|a−b|⇒∣∣−1+i√q−1∣∣=∣∣−1−i√q−1∣∣=∣∣−1+i√q−1+1+i√q−1∣∣⇒1+q−1=4(q−1)⇒q=43 Ans: B