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Find all b for which -x^2+6x+20=b+x^2-4x+8 will have no real roots​

 Apr 24, 2022
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-x^2  + 6x + 20  =  b + x^2 - 4x  + 8      rearrange as

 

2x^2  -  10x   +  (b - 12 )  = 0

 

It will have no real roots  when  the discriminant   is <  0

 

So

 

10^2   -  4(2) (b - 12)  < 0

 

100  - 8b  + 96  <   0

 

196  <  8b

 

8b > 196

 

b >   196/ 8

 

b >  49 /  2

 

It will have no real roots  when    b >  49  / 2

 

 

 

 

cool cool cool 

 Apr 24, 2022

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