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If the roots of the equation $x^{2}-n x+m=0$ differ by 1, then
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Verified Answer
The correct answer is:
$\mathrm{n}^{2}-4 \mathrm{~m}-1=0$
Let the root be $\alpha$ and $\beta$ $x^{2}-n x+m=0$
$\Rightarrow \alpha+\beta=n ; \alpha . \beta=\mathrm{m}$
$\alpha-\beta=$
$\Rightarrow(\alpha+\beta)^{2}=(\alpha-\beta)^{2}+4 \alpha \beta$
$\Rightarrow \mathrm{n}^{2}=1+4 \mathrm{~m}$
- $n^{2}-4 m-1=0$
$\Rightarrow \alpha+\beta=n ; \alpha . \beta=\mathrm{m}$
$\alpha-\beta=$
$\Rightarrow(\alpha+\beta)^{2}=(\alpha-\beta)^{2}+4 \alpha \beta$
$\Rightarrow \mathrm{n}^{2}=1+4 \mathrm{~m}$
- $n^{2}-4 m-1=0$
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