Algebra 2A - Polynomials

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? Justify your answer using mathematical reasoning; try to relate polynomial operations using integer operations as a comparison. Provide many examples (or counterexamples) to help strengthen your argument.

Answer 1

Consider y = x² - 5x + 6 which has real roots 3 and 3.

Add y = 5x which has real root 0

The resulting function is y = x² + 6 which has no real roots.