## Solving Lesson 26 Page 14 Math Workbook 10 – Kite>

Topic

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.