Q64 / 100 · BITSAT 2023 (Memory Based Paper 2) · Mathematics

Solve $\sqrt{5} x^2+x+\sqrt{5}=0$

  • A
    $\pm \frac{\sqrt{19}}{5} \mathrm{i}$
  • B
    $\pm \frac{\sqrt{19} i}{2}$
  • Correct answer
    C
    $\frac{-1 \pm \sqrt{19} i}{2 \sqrt{5}}$
  • D
    $\frac{-1 \pm \sqrt{19} \mathrm{i}}{\sqrt{5}}$

Solution

Here, $\mathrm{b}^2-4 \mathrm{ac}=1^2-4 \times \sqrt{5} \times \sqrt{5}$ $=1-20=-19$
Therefore, the solutions are
$\frac{-1 \pm \sqrt{-19}}{2 \sqrt{5}}=\frac{-1 \pm \sqrt{19 i}}{2 \sqrt{5}}$

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

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