Q43 / 125 · BITSAT 2015 · Mathematics

The root of the equation $2(1+i) x^{2}-4(2-i) x-5-3 i=0$ which has greater modulus is

  • Correct answer
    A
    $\frac{3-5 i}{2}$
  • B
    $\frac{5-3 \mathrm{i}}{2}$
  • C
    $\frac{3-i}{2}$
  • D
    none

Solution

$\begin{aligned} \text { Roots } &=\frac{4(2-i) \pm \sqrt{16(2-i)^{2}+8(1+i)(5+3 i)}}{4(1+i)} \\ &=\frac{4-i}{1+i} \text { or } \frac{-i}{1+i}=\frac{3-5 i}{2} \text { or } \frac{-1-i}{2} \end{aligned}$

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

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