AP EAMCET · Maths · Quadratic Equation
If " \(2 i\) " is a root of \(f(z)=z^4+z^3+2 z^2+4 z-8=0\), then which among the following cannot be a root of \(f(z)=0\) ?
- A \(-2 i\)
- B 1
- C –2
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
It is given that, \(f(z)=z^4+z^3+2 z^2+4 z-8\) have a root \(2 i\), so one more root will be \(-2 i\), so \(\left(z^2+4\right)\) is the factor of \(z^4+z^3+2 z^2+4 z-8\). So, \(z^4+z^3+2 z^2+4 z-8\) \[ =\left(z^2+4\right)\left(z^2+z-2\right) \] and \(z^2+z-2=(z+2)(z-1)\)…
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