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If roots of the equation $x^{2} - b x + c = 0$ be two consecutive integers, then $b^{2} - 4 c$ equals

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answer is D.

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Detailed Solution

$α + α + 1 = \frac{- (- b)}{1}$

$2 α + 1 = b$

$α \cdot (α + 1) = \frac{c}{a}$

$α \cdot (α + 1) = \frac{c}{1}$

$b^{2} - 4 c = {(2 α + 1)}^{2} - 4 (α (α + 1))$

$= 4 α^{2} + 1 + 4 α - 4 (α^{2} + α)$

$= 4 α^{2} + 1 + 4 α - 4 α^{2} - 4 α$

$= 1$ .

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