Question

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

(a) \(\frac{-1±i\sqrt{11}}{6\sqrt{3}}\)

(b) \(\frac{1±i\sqrt{11}}{6\sqrt{3}}\)

(c) \(\frac{1±\sqrt{11}}{6\sqrt{3}}\)

(d) \(\frac{-1±\sqrt{11}}{6\sqrt{3}}\)

The question was posed to me in an interview for job.

Question is taken from Quadratic Equations topic in section Complex Numbers and Quadratic Equations of Mathematics – Class 11

Answer 1

Right option is (a) \(\frac{-1±i\sqrt{11}}{6\sqrt{3}}\)

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

=>3x^2 + √3x + 3 = 0

=>D = (√3)^2 – 4.3.3 = 3-36 = -33.

Since D ≤ 0, imaginary roots are there.

=>x = \(\frac{-\sqrt{3}±i\sqrt{33}}{2.3} = \frac{-1±i\sqrt{11}}{6\sqrt{3}}\).