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Each solution to x^2 + 5x + 8 = -14 can be written in the form a + bi where a and b are real numbers. What is a^2 + b^2?

 Jul 27, 2022
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This problem avoids direct vieta's formulas! Smart!

 

We know that a^2 + b^2 = (a + bi)(a - bi), which are just the product of the roots!

 

x^2 + 5x + 22 = 0

 

By vieta's,  the product of the roots is -22.

 Jul 27, 2022

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