Find the sum of all possible positive integer values of b such that the quadratic equation \(2x^2 + 5x + b = 0\) has rational roots.
+118725 Find the sum of all possible positive integer values of b such that the quadratic equation 2x^2 + 5x + b = 0 has rational roots.
This will have rational roots when
\(25-4*2*b\ge 0\\ 25-8b\ge0\\ -8b\ge-25\\ 8b\le25\\ b\le 3\frac{1}{8} \)
b has to be a positive integer - according to the question so
b can equal 1,2,or 3
1+2+3 = 6
+130561 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
