Question

Solve \(\sqrt{3}x^2 – \sqrt{2} x + 3\sqrt{3}\) = 0

(a) \(\frac{-1±i\sqrt{17}}{2}\)

(b) \(\frac{1±i\sqrt{17}}{2}\)

(c) \(\frac{1±\sqrt{17}}{2}\)

(d) \(\frac{-1±\sqrt{17}}{2}\)

I got this question during an interview for a job.

The question is from Quadratic Equations topic in section Complex Numbers and Quadratic Equations of Mathematics – Class 11

Answer 1

Right choice is (b) \(\frac{1±i\sqrt{17}}{2}\)

The explanation is: \(\sqrt{3}x^2 – \sqrt{2} x + 3\sqrt{3}\) = 0

=>3x^2 – \(\sqrt{6}\)x + 9 = 0

=>D=(-\(\sqrt{6}\))^2 – 4.3.9 = 6-108 = -102.

Since D ≤ 0, imaginary roots are there.

=>x = \(\frac{\sqrt{6}±i\sqrt{102}}{2.3} = \frac{1±i\sqrt{17}}{2}\).