What is the absolute value of the difference between the roots of $x^{2} + 8 x + 7 = 0$ ?

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Solution

$x^{2} + 8 x + 7 = 0$
$\Rightarrow x^{2} + 7 x + x + 7 = 0$
$\Rightarrow$ $x (x + 7) + 1 (x + 7) = 0$
$\Rightarrow$ $(x + 7) (x + 1) = 0$
$∴$ Either $x + 7 = 0$
$\Rightarrow x = - 7$
or $x + 1 = 0$
$\Rightarrow x = - 1$
Hence the required solution are $x_{1} = - 7$ and $x_{2} = - 1$
$∴ | x_{1} - x_{2} | = | - 7 - (- 1) | = | - 6 | = 6$

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