Let λϵR. If the origin and the non-real roots of 2z2+2z+λ=0 form the three vertices of an equilateral triangle in the Argand plane, then λ is
A
1
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B
23
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C
2
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D
−1
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Solution
The correct option is B23 z1z2=λ2 and z1+z2=−1 Now since 0,z1,z2 form an equilateral triangle z1(z2)+z2(0)+z1(0)=z21+z22+02 z21+z22=z2z1 (z1+z2)2−2z1z2=z1z2 1=3z1z2 1=3(λ2) λ=23