Find the proper subsets of { $x$ : $x^{2} - 9 x - 10 = 0$ }.

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Solution

The subsets of a given set other than itself are called proper subsets of the given subset.
Now $x^{2} - 9 x - 10 = 0$
$\Rightarrow x^{2} - 10 x + x - 10 = 0$
$\Rightarrow x (x - 10) + (x - 10) = 0$
$\Rightarrow (x - 10) (x + 1) = 0$
$\Rightarrow x = 10, - 1$
$∴ A = {10, - 1}$
So, proper subsets of the given set are $ϕ,$ { $10$ }, { $- 1$ }

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