# math

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Write a quadratic equation with real coefficients if one of the solutions is -5 + 7i

• math -

complex roots always come in pairs, so the other root is -5 - 7i

sum of roots = (-5+7i) + (-5-7i) = -10
product of roots = (-5+7i)(-5-7i)
= 25 - 49i^2 = 25+49 = 74

equation:
x^2 + 10x + 74 = 0

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