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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

Chapter Review

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Exercise 48 Page 350

Recall the Conjugate Root Theorem.

1+i

Practice makes perfect

We are told that the given roots are roots of a polynomial function P(x) that has rational coefficients. 1-i and 5

To find an additional root of P(x)=0, let's recall the second part of the Conjugate Root Theorem.

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

This means that if a + bi is a complex root, then a - bi is also a root. Let's now use this to find a complex root.

Hypotheses	Conclusion
P(x) has rational, real coefficients	1+i is also a root of P(x)
1-i is a complex root of P(x)	1+i is also a root of P(x)

An additional root that we can know for certain using the Conjugate Root Theorem is 1+i.

Subchapter links

Exercises p.347-352