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

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x = \sqrt{2} \pm 2 i

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

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

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

answer is D.

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Detailed Solution

It is given that the quadratic equation

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

Here we use the quadratic formula to solve the question i.e.

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

.
We know that the standard quadratic equation is

{ax}^{2} + bx + c

.
comparing the given quadratic equation, we find the values of a, b, c to be

a = 1, b = 2 \sqrt{2}

and

c = 6

.
So, by quadratic formula,

⇒ x = − b ± b 2 − 4 a c 2 a ⇒ x = − 22 ± (22) 2 − 4 × 1 × 6 2 × 1 ⇒ x = − 22 ± 8 − 24 2 ⇒ x = − 22 ± − 16 2 ⇒ x = − 22 ± 4 i 2

Thus, the correct answer is

- \sqrt{2} \pm 2 i

.
Hence, the correct option is 4.

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