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Let A be the solution set of the polynomial \(P\left( x \right)\), B be the solution set of the polynomial \(Q\left( x \right)\), D be the solution set of the polynomial \( {P^2}(x) + {Q^2}(x)\). Which of the following sets is D?

A. \(A \cup B\)

B. \(A \cap B\)

C. \(A\backslash B\)

D. \(B\backslash A\)

Detailed explanation

Select REMOVE

Consider P²(x) + Q²(x) = 0

For all real values ​​of x: P²(x) 0 and Q²(x) 0

should leave P²(x) + Q²(x) = 0, then P(x) = Q(x) = 0.

Therefore, the solution of the polynomial \(P(x).Q(x)\) is the solution of the polynomial P(x) and the solution of the polynomial Q(x), so C = A∩B.