Question

Find the root of the quadratic equation $x^2+2\sqrt{2x}+6=0$ 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

Answer: (B)

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

According to the given quadratic equation,

$a=1,b=2\sqrt{2}$ and $c=6$

So, by quadratic formula,

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-2\sqrt{2}\pm \sqrt{(2\sqrt{2}{)}^2-4\times 1\times 6}}{2\times 1}$

$=\frac{-2\sqrt{2}\pm \sqrt{8-24}}{2}=\frac{-2\sqrt{2}\pm \sqrt{-16}}{2}=\frac{-2\sqrt{2}\pm 4i}{2}$

Thus, $x=-\sqrt{2}\pm 2i$