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P(x)=a(x^2 + 1)-x(a^2+1)
=ax^2 + a - a^2 x - x
=ax^2 -a^2 x - x + a
Now,let P(x)=0
hence, x=1/a and x=a
You can verify by substituting these values in the original equation and it will work.
Hope it helps.
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