Question 1151314
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<pre>

Do you know the quadratic formula ?


It has the form       r,s = {{{(-b +- something)/(2a)}}},

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  {{{sqrt(b^2 - 4ac)}}} = {{{sqrt(14^2 - 4*3*(-5))}}} = {{{sqrt(256)}}} = 16.


The "a" is 3.


Therefore, the answer is  {{{16/3}}}.


<U>ANSWER</U>.  The difference r - s = {{{16/3}}}.
</pre>

Solved.


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On quadratic formula, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Introduction-Into-Quadratics.lesson>Introduction into Quadratic Equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/proof-of-quadratic-by-completing-the-square.lesson>PROOF of quadratic formula by completing the square</A>

in this site.