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

Mathematics
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If  has two non-real roots, find all possible values of . Express your answer in interval notation.

Jun 29th, 2015

Thank you for the opportunity to help you with your question!

using quadratic formula
x= [-b+- sqrt(b^2-4ac)]/2a

here 

a=1

b=b

c=9

so

x= [-b+- sqrt(b^2-4(1)(9))]/2(1)

2x+b  = sqrt(b^2-36)      ,                2x+b  = - sqrt(b^2-36)

taking square

(2x+b )^2 = b^2-36            ,                       (-2x-b )^2 = b^2-36

4x^2 + b^2 + 4xb = b^2 -36     ,                 

4x^2+36  = -4xb

b= - [ 4x^2+36/ 4x]

b= - [(x^2+8)/x]

so values of b would be  = {  - (x^2+8)/x }

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Jun 29th, 2015

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