Question

If $b$ and $c$ are odd integers, then the equation $x^2 + bx + c = 0$ has

• A. two odd roots
• B. two integer roots, one odd and one even
• C. no integer roots
• D. none of these

Answer 1

Answer: (C)

no integer roots

Answer 2

If $\alpha , \beta$ are the roots, then $\alpha + \beta = - b$ = An odd integer $\alpha \beta = c$ = An odd integer $\therefore \, \alpha , \beta$ cannot be integers [Both cannot be odd. Also one odd, other even is not possible] $\therefore$ given $= n$ has no integer roots.