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If roots of the equation $x^2-b x+c=0$ be two consectutive integers, then $b^2-4 c$ equals
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Let $\alpha, \alpha+1$ be roots
$$
\begin{aligned}
& \alpha+\alpha+1=b \\
& \alpha(\alpha+1)=c \\
& \therefore b^2-4 c=(2 \alpha+1)^2-4 \alpha(\alpha+1)=1 .
\end{aligned}
$$
$$
\begin{aligned}
& \alpha+\alpha+1=b \\
& \alpha(\alpha+1)=c \\
& \therefore b^2-4 c=(2 \alpha+1)^2-4 \alpha(\alpha+1)=1 .
\end{aligned}
$$
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