If the roots of x^2-bx+c=0 are two consecutive integers, then b^2-4c equals

Question

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

Accepted Answer

Let roots be $\alpha,\alpha+1$: $b=2\alpha+1$, $c=\alpha(\alpha+1)$.

$$b^2-4c=(2\alpha+1)^2-4\alpha(\alpha+1)=1.$$

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