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Question

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 D 43
Let a and b be the roots of the equation z2+2z+q=0
a,b=1±iq1
Since Origin, a & b form an equilateral triangle.
Therefore |a|=|b|=|ab|
|a|=|b|=|ab|1+iq1=1iq1=1+iq1+1+iq11+q1=4(q1)q=43
Ans: B

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