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Form a quadratic polynomial whose zeroes are 3 - sqrt(3)/5 and 3 + sqrt(3)/5.

 Apr 6, 2022
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Let the quadratic be of the form   ax^2 + bx + c

Let us suppose  that the quadratic is monic  ( a =1)   

 

By Vieta....

 

The sum of the roots  =  -b  =    (3 + sqrt 3) / 5   + ( 3 - sqrt 3) / 5   =  3/5 + 3/5  = 6/5

 

So b =  -6/5

 

And the product of the roots  =  c  =  (3 + sqrt 3) / 5   *   (3 - sqrt 3)  / 5 =  [ 9  - 3 ] /25  =  6/25

 

So....the monic polynomial   is

 

x^2  - (6/5)x  + ( 6 / 25 )

 

If we wanted  integer coefficients  we also could have

 

25x^2 - 30x + 6    .......  many other answers are also possible

 

 

cool cool cool

 Apr 6, 2022
edited by CPhill  Apr 6, 2022
edited by CPhill  Apr 6, 2022

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