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Find all values of $q$ such that the quadratic equation $qx^2 + (2q - 9)x + (q - 8) = 0$ has two positive real roots.

 Aug 25, 2023
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Not totally sure about this one......!!!

 

To have two positive real roots,  -( 2q - 9) / q  must be > 0   and  (q - 8) / q  must be > 0

 

-(2q - 9) / q >  0                       (q - 8) / q >  0

9 - 2q > 0                                   q - 8  >  0

9 > 2q                                         q >  8

q < 9/2 

 

No solutions exist  for  q  since these intervals  do  not  intersect

 

 

cool cool cool

 Aug 25, 2023

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