Prove that ax^2 + bx + c = 0 doesn't have rational solutions for any a, b, c odd...

[Lawliet]

"Prove that ax^2 + bx + c = 0 does not have rational solutions for any a,b,c odd integers."
This question is from a regional contest from my country. I have to mention that I cannot use integrals (in case this is the solution someone came up with) because it's not officialy learned at my grade.
Thanks.

 

[Lawliet]

"Prove that ax^2 + bx + c = 0 doesn't have rational solutions for any a, b, c odd integers."
I pretty much know the combinations of addition and multiplication of odd and even numbers, but I definetely don't know where to start on this one. Can someone help me ? I must not use integrals.

 

[stapel]

"Prove that ax^2 + bx + c = 0 doesn't have rational solutions for any a, b, c odd integers."

I pretty much know the combinations of addition and multiplication of odd and even numbers, but I definetely don't know where to start on this one. Can someone help me ? I must not use integrals.

Have you tried anything similar to "Example 3" on this page?

 

[pka]

"Prove that ax^2 + bx + c = 0 does not have rational solutions for any a,b,c odd integers."
This question is from a regional contest from my country.

The only question here is, can \(\displaystyle b^2-4ac\) be a perfect square?