let z be a complex number such that the imaginary part of z is non zero and a= z^2 +z+1 is real. Then a cannot be value
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Answer:
The given equation is z
2
+z+1−a=0
If the solution is not real then Δ=b
2
−4ac of the quadratic ax
2
+bx+c=0 is less than zero.
⇒1−4(1−a)<0
⇒1−4+4a<0
⇒4a<3
⇒a<
4
3
Hence, all values of a less than
4
3
will give non-real solutions.
Options A, B and C are less than
4
3
.
Hence option D is correct
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