document.write( "Question 165853: Can you please help me solve this question? Write a polynomial equation of the least degree with the roots 4,1,i,and -1. \n" ); document.write( "

Algebra.Com's Answer #122337 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Write a polynomial equation of the least degree with the roots 4,1,i,and -1.
\n" ); document.write( ":
\n" ); document.write( "Write factors from the roots
\n" ); document.write( "(x-4)
\n" ); document.write( "(x+1)*(x-1) = (x^2 - 1) = 0
\n" ); document.write( "and
\n" ); document.write( "x = i
\n" ); document.write( "x^2 = i^2
\n" ); document.write( "x^2 = -1
\n" ); document.write( "(x^2+1) = 0
\n" ); document.write( ":
\n" ); document.write( "(x^2-1) * (x^2+1) = x^4 -x^2 + x^2 - 1 = x^4 - 1
\n" ); document.write( "then
\n" ); document.write( "(x-4)*(x^4-1) = x^5 - x - x^4 + 4
\n" ); document.write( ":
\n" ); document.write( "Arrange to: x^5 - 4x^4 - x + 4 \n" ); document.write( "

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