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x = 5 is a root of the polynomial x^2 - 3kx + (k - 1).  What is the other root?

 May 4, 2020
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x^2  -3kx + (k - 1)   = 0

 

By Vieta's Theorem.....the  sum of the roots  =   3k

 

And the product of  the roots  =  k - 1

 

Call  r  the other root

 

So    

 

5 + r  =  3k       ⇒  (5+ r) / 3  =  k

And

5r  = k - 1

 

So....this implies that

5r  =  (5 + r) /3  - 1       multiply through by 3

 

15r  = 5 + r  - 3

 

15r  = 2 + r

 

14r  =  2

 

r  = 2/14   =   1/7

 

 

cool cool cool

 May 4, 2020
edited by CPhill  May 4, 2020

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