Exercise 19 Page 316

Hypotheses	Conclusion
P(x) has rational coefficients	14+sqrt(2) is also a root of P(x)
14-sqrt(2) is an irrational root of P(x)=0	14+sqrt(2) is also a root of P(x)

Hypotheses	Conclusion
P(x) has rational, real coefficients	0+6i=6i is also a root of P(x)
- 6i=0-6i is a complex root of P(x)	0+6i=6i is also a root of P(x)

Hints

Irrational Conjugate Root Theorem
If P(x) is a polynomial with rational coefficients, then any irrational roots of P(x)=0 occur in conjugate pairs.

Conjugate Root Theorem
If P(x) is a polynomial with real coefficients, then any complex roots of P(x)=0 occur in conjugate pairs.