Multiple Choice Questions on If z minus 4 z 2 then the maximum value of z is equal to ........ for NDA Exam Preparation

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Multiple Choice Questions

If z minus 4 z 2 then the maximum value of z is equal to ........

Mathematics (NDA) Quadratic Equations
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    If |z − 4 / z | = 2, then the maximum value of |z| is equal to-

    . 1+ √3

    Incorrect Answer

    1 + √5

    Correct Answer

    1− √5

    Incorrect Answer

    √5 −1

    Incorrect Answer
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    Explanation:

    |z - 4/z | ≥ 2

    Now using property, |z - 4/z | ≥ |z| − | 4/z |

    Or 2    ≥ |z| - 4 / |z|

    Or 2|z| ≥ |z|2 – 4

    Or |z| - 2|z| - 4 ≤ 0

    Or |z| = 2±2√5 / 2 = 1±√5

    Maximum value of |z| is 1+ √5

    By: Yachna
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