document.write( "Question 1095091: Suppose a polynomial function of degree 4 with rational coefficients has the following given numbers as zeros. Find the other​ zero(s).
\n" ); document.write( "i, 7 square root of 11
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Algebra.Com's Answer #709629 by greenestamps(13200)\"\" \"About 
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If a polynomial has rational coefficients, then irrational and complex roots must occur in conjugate pairs.

\n" ); document.write( "In case you aren't familiar with the term conjugate pairs, the conjugate of the complex number a+bi is a-bi; the conjugate of the irrational number a+b*sqrt(c) is a-b*sqrt(c).

\n" ); document.write( "So in your example, with one root i, another root must be -i; and with one root 7*sqrt(11), another root must be -7*sqrt(11).

\n" ); document.write( "The four roots are the conjugate pairs
\n" ); document.write( "(1) i and -i
\n" ); document.write( "(2) 7*sqrt(11) and -7*sqrt(11)
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