The condition for equation $x^{2} - b x + c = 0$ to have two consecutive integers as its roots is

b^{2} - c^{2} = 1

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b^{2} - 4 c = 1

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c^{2} - 4 b^{2} = 1

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b = c

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Solution

The correct option is B $b^{2} - 4 c = 1$
Let $x^{2} - b x + c = 0$ has roots $n, n + 1$
$n + 1 - n = \frac{\sqrt{b^{2} - 4 a c}}{a} = \frac{\sqrt{b^{2} - 4 c}}{1}$
$⟹ b^{2} - 4 c = 1$

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