SOLUTION: Show that {{{f(x)=x^2+6x+12}}} is always positive for all values of x

Question 1135104: Show that is always positive for all values of x
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.

 =  + 3 =  + 3.


So, this expression is the sum of two terms.


First term is quadratic binomial  ,  which ALWAYS is non-negative as a square of a real number.


The second term is constant term "3", which is positive, too.


Therefore, their sum is ALWAYS positive.


Thus, the original expression is always positive, too.

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It is a TEMPLATE and a SAMPLE to you on how this and similar problems should be solved and worded.

The method which I used is called "completing the square".

On how this method works, you can read from the lesson
- HOW TO complete the square - Learning by examples
in this site.

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