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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: find the value of k that makes the sum of the roots of 3x^2-(3k+2)x+18=0 equal to 6.      Log On


   

Question 891091: find the value of k that makes the sum of the roots of 3x^2-(3k+2)x+18=0 equal to 6.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Roots, x=%283k%2B2%2B-+sqrt%28%283k%2B2%29%5E2-4%2A3%2A18%29%29%2F%282%2A3%29

Simplify the discriminant, %289k%5E2-12k%2B4%29-216=9k%5E2-12k-212

Now you want %283k%2B2-sqrt%289k%5E2-12k-212%29%29%2F6%2B%283k%2B2%2Bsqrt%289k%5E2-12k-212%29%29%2F6=6

%286k%2B4%2B0%29%2F6=6
6k%2B4=36
3k%2B2=18
3k=16
highlight%28k=16%2F3%29



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Notice, doing much of anything with the discriminant was not needed.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
find the value of k that makes the sum of the roots of 3x^2-(3k+2)x+18=0 equal to 6.


3x%5E2+-+%283k+%2B+2%29x+%2B+18+=+0



Sum of roots = -+b%2Fa

6+=+-+%28-+%283k+%2B+2%29%29%2F3 ------ Substituting sum of roots value, b and a

6+=+%283k+%2B+2%29%2F3+

3k + 2 = 18 ------- Cross-multiplying 

3k = 16

highlight_green%28highlight_green%28k+=+16%2F3%29%29