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# Complex Roots

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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 + b^2?

Sep 21, 2021

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What is a + b^2?

Hello Guest!

$$x^2 + 5x + 8 = -14\\ x_{1,2}= \frac{1}{2}(-5\pm 3\sqrt{7}i)\\ x_1=a+b_1i=-\frac{5}{2}+\frac{3\sqrt{7}i}{2}\\ {\color{blue}a+b_1^2}=-\frac{5}{2}+\frac{63}{4}\color{blue}=\dfrac{53}{4}$$

$$x_2=a+b_2i=-\frac{5}{2}-\frac{3\sqrt{7}i}{2}\\ {\color{blue}a+b_2^2}=-\frac{5}{2}+\frac{63}{4}\color{blue}=\dfrac{53}{4}$$

!

Sep 22, 2021
edited by asinus  Sep 22, 2021
edited by asinus  Sep 22, 2021