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