Algebra 2 Question

Question

If two polynomial equations have real solutions, then will the equation that is the result of adding, subtracting, or multiplying the two polynomial equations also have real solutions? Will the resulting equation have complex solutions if one or both of the original equations have complex solutions?

Answer 1

As a partial answer, consider

p(x) = 25 - x² which has zeros ±5 and

q(x) = 2x² - 10 which has zeros ±√5

 

p(x) + q(x) = x² + 15 which has no real zeros.