Multiple choice

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

  1. $x = \sqrt 2 \pm 2i$
  2. $x = - \sqrt 2 \pm 2i$
  3. $x = - \sqrt 4 \pm 2i$
  4. $x = - \sqrt 2 \pm 4i$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quadratic formula: x = [-b +/- sqrt(b^2 - 4ac)] / 2a. a=1, b=2*sqrt(2), c=6. x = [-2*sqrt(2) +/- sqrt(8 - 24)] / 2 = [-2*sqrt(2) +/- sqrt(-16)] / 2 = [-2*sqrt(2) +/- 4i] / 2 = -sqrt(2) +/- 2i.

AI explanation

Assuming the intended equation is x^2 + 2*sqrt(2)*x + 6 = 0, apply the quadratic formula with a = 1, b = 2*sqrt(2) and c = 6. The discriminant is (2*sqrt(2))^2 - 4(1)(6), which evaluates to 8 - 24, or -16. Taking the square root of -16 gives 4i, so the roots evaluate to (-2*sqrt(2) +/- 4i) / 2, making the final roots x = -sqrt(2) +/- 2i.