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

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Solution

${x : x^{2} - 9 x - 10 = 0} x^{2} - 9 x - 10 = 0 \Rightarrow x^{2} - 10 x + x - 10 = 0 \Rightarrow x (x - 10) + 1 (x - 10) = 0 \Rightarrow (x - 10) (x + 1) = 0 ∴ E i t h e r x - 10 = 0 o r x + 1 = 0 \Rightarrow x = 10 \Rightarrow x = - 1 ∴ G i v e n s e t = {- 1, 10} ∴ P r o p e r s u b s e t s o f t h i s s e t = ϕ, {- 1}, {10}$

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