Solve the equation
$5^{x^{2} + 3 x + 2} = 1$
find the difference between the roots of the equation.

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Solution

$5^{x^{2} + 3 x + 2} = 1$
$\Rightarrow x^{2} + 3 x + 2 = 0 \Rightarrow (x + 1) (x + 2) = 0$
$∴ x_{1} = - 1, x_{2} = - 2$
Consequently
this equation has two roots $x_{1} = - 1,$ and $x_{2} = - 2$

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