If x^2+bx+9 has two non-real roots, find all possible values of b.

We want the discriminant to be negative, so we want

b² - 4(1)(9)  <  0

b² - 36  <  0

b²  <  36

This is true when...

| b |  <  6

Which is true when...

b < 6     and     b > -6

So  b  is any number in the interval  (-6, 6)

(The endpoints are not included because that makes the discriminant equal to zero, which gives only one real root to the original polynonmial.)

Check:  https://www.desmos.com/calculator/q4gcahv61l

Try moving the slider for  b  and notice that only and for all  b  values in the interval  (-6, 6) , the graph is entirely above the x-axis.

We want b^2 <= 9, so the answer is [-3,3].

Htyhang919     You are one extremely rude person!

You delete your question after Hectictar has put in all that effort to answer it .   How incrdeibly RUDE.

I see you have done it on your other questions too.

I guess you have been caught cheating or you are frightened that you will be. 

JUST HOW RUDE !!!

Here’s a copy of the original question.

If x^2+bx+9 has two non-real roots, find all possible values of b. Express your answer in interval notation.

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You know you are not supposed to post AoPS questions. You chose to do so, anyway. You then delete your questions because you fear getting caught, or you do not want anyone else to benefit from the solution.  This makes you an APoS (A Piece of Shit) student.

Andre Mossow, the webmaster, bans members for deleting question. https://web2.0calc.com/questions/change-username#r2

 If you do this again, you’ll be gone.  Good riddance!

GA