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Find the sum of all possible positive integer values of b such that the quadratic equation 2x^2 + 15x + b = 0 has rational roots.

 Nov 5, 2021
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2x^2 + 5x + b  = 0

 

If b is a positive integer.......it cannot be an integer larger than 3 because the discriminant  would be < 0

 

So......the only possible positive integer values for b are either 1, 2 or 3

 

If b =  1, the discriminant   =  √17 and this will  not  produce a rational  solution

 

If b = 2, the discriminant = √9  = 3    and this will produce a rational  solution

 

And if b = 3, the discriminant   = √1   = 1   and this too will produce a rational solution

 

So....2,3 produce rational roots for b....where b is a positive integer

 

And the sum of these  = 5

 Nov 5, 2021

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