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Find the quadratic with integer coefficients whose roots are \(\dfrac{-7 \pm \sqrt{23} i}{2}\)

 Jul 28, 2020
 #1
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Here is one way to find the quadratic

 

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)   =  (7+- sqrt23i)/2        so  a  =1   and b = -7

 

x^2 -7x + c              to find c      sqrt(  -7^2-4(1)(c))  = sqrt 23i        

                                  solving for c = 18

 

x^2-7x+18 =0                            

 Jul 28, 2020

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