document.write( "Question 255669: find an nth degree polynomial function with real coefficients satisfying the given conditions: n=3; 2 and 5i are zeros; f(-1)=156. \n" ); document.write( "

Algebra.Com's Answer #187904 by drk(1908) $\"\"$ $\"About$

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n=3; We need a third degree polynomials with the following given zero's: 2 and 5i are zeros; f(-1)=156.
\n" ); document.write( "Since these are solutions
\n" ); document.write( "x = 2 ; x = 5i. Since imaginaries travel in pairs, the other answer is x= -5i.
\n" ); document.write( "We have (x-2)(x-5i)(x+5i) = 0
\n" ); document.write( "Now,
\n" ); document.write( "f(-1) = (-1-2)(-1-5i)(-1+5i) = 156.
\n" ); document.write( "f(-1) = (-3)(26) = -78.
\n" ); document.write( "But -78 x -2 = 156, so our polynomial becomes
\n" ); document.write( " $\"Y+=+-2%28x-2%29%28x%5E2+%2B+25%29+=+0\"$ \n" ); document.write( "

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