2-5 Fundamental Theorem of Algebra
2-5 Fundamental Theorem of Algebra
2-5 Fundamental Theorem of Algebra
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Conjugate pairs: a + bi and a - bi<br />
Complex numbers occur in conjugates pairs<br />
Let f(x) be a polynomial function that has real coefficients.<br />
If a + bi, where b does not equal 0, is a zero <strong>of</strong> the function,<br />
the conjugate pair a - bi is also a zero <strong>of</strong> the function.<br />
Ex. 4 Find a 4th degree polynomial function with real coefficients,<br />
that has 1, -1, and 3i as zeros.<br />
f(x) = (x+1)(x-1)(x-3i)(x+3i)=<br />
4
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