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If 3 + 2i is a solution for x^2 + bx + c = 0, where b and c are real numbers, then what are b and c?

 Jun 7, 2022
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If 3 + 2i  is a root  then so is 3 - 2i

 

By Vieta

 

ax^2 + bx + c  = 0

 

Sum of the roots =  -b/a           and a  =1

So   (3 + 2i)  + (3 -2i)  = 6/1   = -b/1   → b = -6

 

Product of the roots =   c/a

So (3+2i)(3-2i)  =  9 - 4i^2  =  9 -4(-1)  = 9 + 4 = 13  =    13/1  →   13  =  c  

 

 

cool cool cool

 Jun 7, 2022

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