Question Detail
Question
Determine the moduli for the complex roots of the quadratic equation given by: \(x^2 - 4x + 13 = 0\)
Correct Answer
Option B is the correct answer.
Detailed Explanation
Roots: (x = \frac{4 \pm \sqrt{16-52}}{2} = \frac{4 \pm \sqrt{-36}}{2} = \frac{4 \pm 6i}{2} = 2 \pm 3i). Modulus of each root: (\sqrt{2^2 + 3^2} = \sqrt{4+9} = \sqrt{13}). So both moduli are (\sqrt{13}).
Hint
Find the roots using the quadratic formula, then compute \(\sqrt{a^2+b^2}\).