Question 1177575
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            I will show you a  STANDARD   and very  SIMPLE  WAY, 

            on how this problem  (and many other similar problems)  should be treated.



<pre>
Since the problem talks about different real roots of a quadratic equation, it means that its discriminant is positive.


The discriminant is  b^2 - 4ac = k^2 - 4*36 = k^2 - 144.


So, the discriminant must be positive

    k^2 - 144 > 0.



It implies

    k^2 > 144, 



which means that  EITHER k > 12  OR  k < - 12.



<U>ANSWER</U>.  The set of all possible values of k is  { k |  k > 12  or  k < - 12 }.


         It is the union of two infinite semi-intervals  (-oo,12) U (12,oo).
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Solved.