Q161 / 270 · NDA 2023 (Phase 1) · Mathematics

If $2-i \sqrt{3}$ where $i=\sqrt{-1}$ is a root of the equation $x^2+a x$ $+b=0$, then what is the value of $(a+b)$ ?

  • A
    $-11$
  • B
    $-3$
  • C
    $0$
  • Correct answer
    D
    $3$

Solution

If $2-\sqrt{3} i$ is one root. $\Rightarrow \quad 2+\sqrt{3} i$ is other root $\therefore \quad-a \mathrm{C}=$ Sum of roots $\Rightarrow-\mathrm{a}=2-\sqrt{3} i+2+\sqrt{3} i=4 \Rightarrow a=-4$ and $b=$ product of roots $b=(2-\sqrt{3} i)(2+\sqrt{3} i)=4+3=7$ $a+b=-4+7=3$

Hence, the correct answer is option: 'D'.

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