document.write( "Question 236848: givn one zero, find all other zeros that can be either real or complex.
\n" ); document.write( "p(x)=x^4-x^3+7x^2-9x-18 (3i is a zero) \n" ); document.write( "

Algebra.Com's Answer #174231 by jim_thompson5910(35256) $\"\"$ $\"About$

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Hint: Recall that all complex zeros come in conjugate pairs. So -3i is also a zero. Now if $\"x=3i\"$ , then $\"x%5E2=-9\"$ and $\"x%5E2%2B9=0\"$ . Now just perform polynomial long division to simplify $\"%28x%5E4-x%5E3%2B7x%5E2-9x-18%29%2F%28x%5E2%2B9%29\"$ . This will basically factor $\"x%5E4-x%5E3%2B7x%5E2-9x-18\"$ into two quadratics, which are easily solved by the quadratic formula. \n" ); document.write( "

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