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

- 2

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3

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2

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1

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Solution

The correct option is D $1$
Given equation is $x^{2} - b x + c = 0$
Let the roots be $α$ and $α + 1$
Therefore, $2 α + 1 = b$
$\Rightarrow α (α + 1) = c$
Hence, $b^{2} - 4 c$
$= (2 α + 1)^{2} - 4 α (α + 1)$
$= 1$

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