SOLUTION: If r and a represent the solutions of the equation (3k + 14) * k = 5 and r > s, what is the value of the difference of r - s?

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Question 1151314: If r and a represent the solutions of the equation (3k + 14) * k = 5 and r > s, what is the value of the difference of r - s?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

Do you know the quadratic formula ?


It has the form       r,s = ,

where b is the coefficient at "k" and "a" is the coefficient at "k^2" in the standard form equation.


When you subtract  r-s, you will get this "something", divided by "a".


Now, the standard form of the equation is


    3k^2 + 14k - 5 = 0.


The "something" is the square root of the discriminant   =  =  = 16.


The "a" is 3.


Therefore, the answer is  .


ANSWER.  The difference r - s = .

Solved.

---------------

On quadratic formula, see the lessons
    - Introduction into Quadratic Equations
    - PROOF of quadratic formula by completing the square
in this site.


Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


If r and s represent the solutions of the equation (3k + 14) * k = 5 and r > s, what is the value of the difference of r - s?








or

So r = 1/3 and s = -5; and the difference r-s is 1/3+5 = 16/3.

Alternatively, we can find the value of r-s without factoring.

The solutions to the equation



are

and

The difference between the two roots is then



For the quadratic in this problem that difference is
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