Maths · Quadratic equations in real and complex number systems and their solutions

Find the root of the quadratic equation by using the quadratic formula

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

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

Step-by-step solution

Given quadratic: x² + 2√2 x + 6 = 0. Using quadratic formula: x = [-b ± √(b² - 4ac)] / (2a) with a=1, b=2√2, c=6. Compute discriminant: b² - 4ac = (2√2)² - 4·1·6 = 8 - 24 = -16. √(-16) = 4i. Then x = [-2√2 ± 4i] / 2 = -√2 ± 2i.
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