If is a complex constant such that z^2+z+ =0 has a real root then

JEE Advanced Mathematics question

If is a complex constant such that has a real root then

Answer: (A),(C),(D)

Let be the real root and . Then

(p++c+(p-iq)=0\ ⇒\ +c+p)+i -1)=0 .

Equating real and imaginary parts: and . Since is nonreal, , so , i.e. . Hence — (d) is correct.

Putting back into the equation: $α+c

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Question ID VK-108119