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JEE Advanced 2012Paper 1
Exam
JEE Advanced
Year
2012
Paper
Paper 1
Subject
Mathematics
Chapter
Complex Number

JEE Advanced 2012 · Paper 1 · Mathematics · Complex Number

Let z be a complex number such that the imaginary part of z is...

Let zz be a complex number such that the imaginary part of zz is non-zero and a=z2+z+1a=z^{2}+z+1 is real. Then a cannot take the value

Options

  1. A−1-1
  2. B13\frac{1}{3}
  3. C12\frac{1}{2}
  4. D34\frac{3}{4}

Correct answer

D. 34\frac{3}{4}

Step-by-step solution

∵Im⁡(z)≠0\because \quad \operatorname{Im}(z) \neq 0 ⇒z\Rightarrow \quad z is non-real and equation z2+z+(1−a)=0z^{2}+z+(1-a)=0 will have non-real roots, if D<0D < 0 ⇒1−4(1−a)<0\Rightarrow \quad 1-4(1-a) < 0 ⇒4a<3⇒a<34\Rightarrow \quad 4 a < 3 \Rightarrow a < \frac{3}{4} ∴a\therefore \quad a can not take the value 34\frac{3}{4}.
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