If the roots of the equation $x^2-bx+c=0$ are two consecutive integers, then $b^2-4c$ is equal to

Solution

1. Let the roots be $k$ and $k+1$ for some integer $k$.
2. The discriminant $D$ of the quadratic equation $x^2-bx+c=0$ is given by $D=b^2-4c$.
3. For a quadratic with roots $r_1$ and $r_2$, $D=(r_1-r_2{)}^2$.
4. Substituting the roots, $$\begin{array}{rl}D& =(k+1-k{)}^2\\ & =1^2\\ & =1\end{array}$$.
5. Hence the answer is (B).