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Find the common zeroes of the polynomialsx^(3)+x^(2)-2x-2 and x^(3)-x^(2)-2x+2.

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Solution :For the common zeroes, first we FIND the H.C.F. of GIVEN polynomials by Euclid's DIVISION method (long division method)
Polynomials

Hence, the H.C.F. of the given polynomials is `(x^(2)-2)`. Thus, the common zeroes of the given ploynomials are the zeroes of `x^(2)-2` i.e.., zeroes of `(x+sqrt(2))(x-sqrt(2))`.
So, common zeroes are `sqrt(2)` and `-sqrt(2) ""` Ans.


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