document.write( "Question 288826: Suppose that a polynomial function of degree 5 with rational coefficients has the numbers $\"+1%2F2+\"$ , $\"+2%2B+sqrt+%28+7+%29+\"$ , $\"+1-3i+\"$ as zeros. Find other zeros.\r
\n" ); document.write( "\n" ); document.write( "I am not positive what Degree 5 means, and although I could find the zeros through trial and error, I know there is some process a bit easier, could you show me? \n" ); document.write( "

Algebra.Com's Answer #209397 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
A degree of 5 means the highest exponent in the polynomial is 5. The degree also tells you how many roots/zeros it has.

\n" ); document.write( "With rational coefficients, the zeros with square roots will come in conjugate pairs: (p+q) and (p-q). This is true because when you multiply (p+q)(p-q) you get $\"p%5E2-q%5E2\"$ which is an expression of perfect squares. This means the square roots will disappear (which needs to happen if there are rational coefficients).

\n" ); document.write( "You are given one rational zero, 1/2, and two zeros with square roots:
\n" ); document.write( " $\"2%2Bsqrt%287%29\"$
\n" ); document.write( "and
\n" ); document.write( "1-3i (Remember that \"i\" is a square root! It is $\"sqrt%28-1%29\"$ .)
\n" ); document.write( "There are 5 zeros in a polynomial of degree 5 so there two missing zeros. They will be the other \"half\" of the respective conjugate pairs:
\n" ); document.write( " $\"2-sqrt%287%29\"$
\n" ); document.write( "and
\n" ); document.write( "1+3i \n" ); document.write( "

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