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

Guest Feb 27, 2022

#1**+1 **

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

Guest Feb 28, 2022

#2**+2 **

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

ElectricPavlov
Feb 28, 2022

#3**+2 **

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.

Alan Feb 28, 2022

#4**+1 **

**Thanx , Alan.**.... I frequently seem to transpose irrational and complex numbers.....

I edited my answer above to be correct ...I think !

ElectricPavlov
Feb 28, 2022

#6**+1 **

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 !

ElectricPavlov
Feb 28, 2022