The roots of the quadratic equation z^2 + az + b = 0 are -7 + 3i and -7 - 3i. What is a + b?

Guest Jan 28, 2022

#1**0 **

z^{2} +az + b = 0, roots are p and q

p + q = -a, pq = b

(-7 + 3i) + (-7 - 3i) = -14 = -a => a = 14

(-7 + 3i)(-7 - 3i) = 49 - 9(-1) = 58 = b => b = 58

z^{2} + 14z + 58 = 0 => \(x = {-14 \pm \sqrt{14^2-4(1)(58)} \over 2(1)} \)

\(x = {-14 \pm \sqrt{-36} \over 2} \)

z = (-7 + 3i) or (-7 - 3i)

Guest Jan 29, 2022