Find the sum of all possible positive integer values of b such that the quadratic equation 2x^2 + 15x + b = 0 has rational roots.
Rational roots means the discriminatn of the quadratic formula is > 0
15^2 - 4(2)(b) > 0
225/ 8 > b
28.125 > b sum 1 - 28 for the answer
+37153 Rational roots means the discriminant of the quadratic formula is >= 0
15^2 - 4(2)(b) >= 0
225/ 8 >= b
28.125 >= b
As alan correctly points out below ..... this will give some irrational numbers
The values between 1 and 28 that give RATIONAL numbers would be
0 1 4 9 16 and 25 I believe .... add 'em up
~ EP
+33661 Hmm. For the roots of the equation to be rational it requires more than just that the discriminant is greater than or equal to zero. It also requires that the square root of the discriminant is not irrational.
+37153 Thanx , Alan..... I frequently seem to transpose irrational and complex numbers.....
I edited my answer above to be correct ...I think !
+37153 Ahhh.... I get it now
sqrt (225-8b) >0 and a perfect square (to be RATIONAL)
But this needs to be a perfect square
so b = 7 13 18 22 25 27 28 Thanx, Alan !
