SOLUTION: If a, b, c are odd integers, then the equation ax2 + bx + c = 0 has no integer solution. How can I prove this? Sorry if its the wrong section >.<

Question 1006071: If a, b, c are odd integers, then the equation ax2 + bx + c = 0 has no integer solution.
How can I prove this?
Sorry if its the wrong section >.<
Answer by ikleyn(52790) (Show Source): You can put this solution on YOUR website!
.
If a, b, c are odd integers, then the equation ax2 + bx + c = 0 has no integer solution.
-----------------------------------------------------------------

Proof

Write the equation in the form

 = .

If x is even then the left side is even, while the right side is odd. Contradiction.

If x is odd, then the left side is even, while the right side is odd. Contradiction again.

Hence, the equation has no solution(s) under the given conditions.

The proof is completed.

RELATED QUESTIONS
If a, b, c are odd integers, then the equation {{{ ax^2+bx+c=0 }}} has no FRACTION... (answered by ikleyn,richard1234)

If a, b, c are odd integers, then the equation {{{ ax^2 + bx + c = 0 }}} has no integer... (answered by jim_thompson5910)

� If you are looking at a graph of a quadratic equation y = ax2 + bx + c, how do you... (answered by stanbon)

If you are looking at a graph of a quadratic equation y = ax2 + bx + c, how do you... (answered by stanbon)

b=a+c, than the equation ax2+bx+c=0 has a) real root b)no real root c) equal root d)... (answered by Theo)

Given odd integers a, b, c, prove that the equation {{{ax^2+bx+c=0}}} cannot have a... (answered by richard1234,ikleyn)

If the solutions to a quadratic equation are - 3 and + 4, what is the equation? Be... (answered by josgarithmetic)

Here is my problem. I have state the problem, as it has been put to us and just below... (answered by stanbon)

Write the equation of a parabola in the form y=ax2 + bx + c where a,b, and c are integers (answered by josh_jordan)