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-2 and 3 are the roots of ax^2 + bx + c = 0.  What are the roots of cx^2 + bx + a?

 May 4, 2020
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The sum of the roots  =  -b/a

So  3 - 2  =  -b/a   =  1      which implies  that  -a  = b

The product of the roots = c/a

So   (-2)(3)   = c/a

-6 = c/a

-6a  = c

 

In the second polynomial we  have that

 

-6ax^2  - ax + a  =  0      divide through by a

 

-6x^2  - x  + 1  =  0

 

6x^2  + x - 1  =  0

 

(3x -1) (2x + 1)  =  0

 

Set both factors to 0  and solve for  x  and we have that

 

x = 1/3      and  x   =  -1/2

 

Just the reciprocals of the original roots....that's a neat result   !!!!!

 

 

cool cool cool

 May 4, 2020

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