document.write( "Question 1095516: Can you help me find a third degree polynomial with a polynomial function with real coefficients that has -3 and i as zeros and such that f(1) =8? \n" ); document.write( "

Algebra.Com's Answer #710027 by greenestamps(13200) $\"\"$ $\"About$

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If the polynomial has real coefficients, then complex or imaginary roots must occur in conjugate pairs. So if i is a root, -i is another root.

\n" ); document.write( "That makes the three roots -3, i, and -1; the polynomial is of the form
\n" ); document.write( " $\"f%28x%29+=+a%28x%2B3%29%28x-i%29%28x%2Bi%29\"$
\n" ); document.write( "where a is a constant.

\n" ); document.write( "The value of the constant a is determined using the given information that f(1) is 8. So to find the value of a and thus finish finding the exact polynomial, solve the equation f(1) = 8:
\n" ); document.write( " $\"a%281%2B3%29%281-i%29%281%2Bi%29+=+8\"$

\n" ); document.write( "I'll let you finish from there.... \n" ); document.write( "

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