Question

Solve 2x^2+√2x+2= 0.

(a) \(\frac{-1±i\sqrt{7}}{2\sqrt{2}}\)

(b) \(\frac{1±i\sqrt{7}}{2\sqrt{2}}\)

(c) \(\frac{1±\sqrt{7}}{2\sqrt{2}}\)

(d) \(\frac{-1±\sqrt{7}}{2\sqrt{2}}\)

I got this question during an online interview.

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

Answer 1

Right choice is (a) \(\frac{-1±i\sqrt{7}}{2\sqrt{2}}\)

To explain: 2x^2+√2x+2 = 0

=>D=(\(\sqrt{2}\))^2 – 4.2.2 = 2-16 = -14.

Since D ≤ 0, imaginary roots are there.

=>x = \(\frac{-\sqrt{2}±\sqrt{D}}{2.2} = \frac{-\sqrt{2}±i\sqrt{14}}{4} = \frac{-1±i\sqrt{7}}{2\sqrt{2}}\).