Hello. Having some trouble proving this problem: If a,b, and c are real numbers

Question

Hello. Having some trouble proving this problem:

If a,b, and c are real numbers with a not equal 0, prove that the function f(x) = ax^2 + bx + c does not have any even roots if c is odd.

Not really sure how to start.

Explanation / Answer

suppose there exists an even solution p [==> a(p^2)+bp +c =0] => a(p^2) = even (since p is even, a is an intezer) =>b*p = even (since p is even, b is an intezer) => a(p^2)+ b*p = even (sum of two even is a even nuber) => -c = even [since p is solution ==> a(p^2)+bp +c =0 +c =0 ==>a(p^2)+bp = -c] => c = even (if a is even so is -a) but c is odd, hence we get a contradiction that there is a even solution hence proved that there is no even solution

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.