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Question reinstated by Melody.

 

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

 Nov 14, 2019
edited by htzhang919  Nov 16, 2019
edited by htzhang919  Nov 16, 2019
edited by Melody  Nov 16, 2019

Best Answer 

 #2
avatar+8829 
+2

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.

 Nov 14, 2019
 #1
avatar
0

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

 Nov 14, 2019
 #2
avatar+8829 
+2
Best Answer

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.

hectictar Nov 14, 2019
 #3
avatar+106027 
0

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 !!!

 Nov 16, 2019
 #4
avatar+1816 
0

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.

***************

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

 Nov 16, 2019
edited by GingerAle  Nov 16, 2019
 #5
avatar+106027 
0

He has already done it for all his questions Ginger.

Melody  Nov 16, 2019

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