TS EAMCET · Maths · Complex Number
The common roots of the equations \(z^3+2 z^2+2 z+1=0\) and \(z^{2018}+z^{2017}+1=0\) satisfy the equation
- A \(z^2-z+1=0\)
- B \(z^4+z^2+1=0\)
- C \(z^6+z^3+1=0\)
- D \(z^{12}+z^6-1=0\)
Answer & Solution
Correct Answer
(B) \(z^4+z^2+1=0\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{array}{rlrl} & & z^3+2 z^2+2 z+1 & =0 \\ \Rightarrow & z^3+1+2 z(z+1) & =0 \\ \Rightarrow & (z+1) & \left(z^2-z+1\right)+2 z(z+1) & =0 \\ \Rightarrow & & (z+1)\left(z^2-z+1+2 z\right) & =0 \\ \Rightarrow & & (z+1)\left(z^2+z+1\right) & =0 \end{array} \] So,…
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