Question

Find the roots of the quadratic equation $x^2+2\sqrt{2}x+6=0$ by using the quadratic formula

• A. $x=\sqrt{2}\pm 2i$
• B. $x=-\sqrt{2}\pm 2i$
• C. $x=-\sqrt{4}\pm 2i$
• D. $x=-\sqrt{2}\pm 4i$

Answer 1

The correct option is B $x=-\sqrt{2}\pm 2i$

Given equation is:

$x^2+2\sqrt{2}x+6=0$

By using quadratic formula,

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\therefore x=\frac{-2\sqrt{2}\pm \sqrt{\left(4\right)\left(2\right)-\left(4\right)\left(1\right)\left(6\right)}}{2\left(1\right)}$

$x=\frac{-2\sqrt{2}\pm 2\sqrt{2-6}}{2}$

$x=\frac{-2\sqrt{2}\pm 2\sqrt{-4}}{2}$

$x=\frac{-2\sqrt{2}\pm 4i}{2}$

$\therefore x=-\sqrt{2}\pm 2i$