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Let $a$ and $b$ be real numbers. Among the four roots of \[z^4 + 4iz^3 - 24z^2 + aiz + b = 0,\]one has real part 1, and another root has real part $-5.$ Enter all possible values of $b,$ separated by commas.

 

I know that if I substitute $z=xi.$, I get 

 

\[x^4 + 4x^3 + 24x^2 - ax + b = 0\]

 

However, I can't figure out how to solve it from there.

 Jan 22, 2021
edited by Guest  Jan 22, 2021
 #1
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By Vieta's formulas, the possible values of b are 22 and 60.

 Jan 22, 2021
 #2
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That's not correct. :(

 

Shouldn't there be 4, since the power of x is 4?

Guest Jan 22, 2021
edited by Guest  Jan 22, 2021

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