document.write( "Question 428149: Suppose that a polynomial function of degree 5 with rational coefficients has 2-3i, -5 and the square root of 7 as zeros. Find the other zeros.\r
\n" ); document.write( "\n" ); document.write( "I am having a terrible time with this problem. I understand the degree of 5 means there are five zeros. I believe the answer is 2+3i and - square root of 7. Help me step by step this please.\r
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Algebra.Com's Answer #297673 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Your answer is exactly correct. For a polynomial equation with real coefficients, complex roots always occur in conjugate pairs. The irrational conjugate roots theorem says: Let

be any polynomial with rational coefficients. If

is a root of

, where

is irrational and

and

are rational, then another root is

.\r
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\n" ); document.write( "\n" ); document.write( "So, if you have a complex root

then you are guaranteed to have another complex root

. Likewise, if you have an irrational root

where

and

, then you are guaranteed to have another irrational root

\r
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\n" ); document.write( "\n" ); document.write( "Therefore

is a root guarantees that

is a root and

guarantees

\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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$\"The$

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