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Find all the values of m for which the equation m(x)^2 + 3x + 1 − m = 0 has no real solutions.

 Nov 24, 2020
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This will have no real solutions when  the discriminant  is  <  0 

 

So  

 

(3)^2  - 4(m) (1 - m)   <  0

 

9  - 4m + 4m^2   <  0

 

4m^2  - 4m  + 9  <  0

 

Looking at the graph here and subbing x  for m,note that this function is  always >  0

 

https://www.desmos.com/calculator/q6jmvmvy7y

 

So....no values of m  give non-real solutions

 

cool cool cool

 Nov 24, 2020

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