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If x^2+bx+16 has at least one real root, find all possible values of b. Express your answer in interval notation.

 Jan 16, 2018
 #1
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x^2  +  bx +  16

 

If it has one (repeated) root  then  the discriminant  is  = 0

 

b^2   -  4(1)(16)   =  0

b^2   -  64  =  0            add 64 to both sides

b^2  =   64                    take both roots

b  =  ±√64

b  = ±8

 

If it has two  roots, then the discriminant  is >  0

 

b^2  -  64  >  0

b^2  > 64

So.....   b < -8    or  b >  8

 

In interval notation, we have     (-inf, -8)   U  (8, inf)

 

 

 

cool cool cool

 Jan 16, 2018

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