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If the roots of $a^{2} x^{2} - a b x + c = 0$ are consecutive integers, then $b^{2} - a^{2}$ =

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answer is D.

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Detailed Solution

$| α - β | = 1$ $\Rightarrow \frac{\sqrt{∆}}{|a|}$

$\Rightarrow \frac{\sqrt{a^{2} b^{2} - 4 a^{2} c}}{a^{2}} = 1$

$\Rightarrow \sqrt{b^{2} - 4 c} = a$

$\Rightarrow b^{2} - a^{2} = 4 c$

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