SOLUTION: find the value of k that makes the sum of the roots of 3x^2-(3k+2)x+18=0 equal to 6.

We make the left side into a "monic" polynomial.  A "monic" polynomial
is one with the coefficient of the term with the greatest degree as 1.
So we divide each coefficient by 3:





In a "monic" polynomial of degree n, the coefficient of the term in
xn-1 is -1 times the sum of the roots of the polynomial.

So the sum of the roots is  = 

Set this equal to 6:



 





Edwin