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# Algebra

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

Jan 28, 2022

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z2 +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

z2 + 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)

Jan 29, 2022