document.write( "Question 1160754: Check that (2+i) is a root of z^4+2(z^3)-9(z^2)-10z+50=0. Find the remaining three roots. \n" ); document.write( "

Algebra.Com's Answer #784166 by MathTherapy(10555) $\"\"$ $\"About$

You can put this solution on YOUR website!
Check that (2+i) is a root of z^4+2(z^3)-9(z^2)-10z+50=0. Find the remaining three roots.
\n" ); document.write( "


\n" );
document.write( "As 1 root is 2 + i, its conjugate/other root is: 2 - i
\n" );
document.write( "With  2 + i and 2 - i being roots, we get: z = 2 + i and z = 2 - i, and so, FACTORS are: z - 2 - i and z - 2 + i.
\n" );
document.write( "The above expands to 
\n" );
document.write( "Using synthetic division or long division of polynomials, we find that the quotient is: .
\n" );
document.write( "Now, since this quotient CANNOT be factored, you can use the quadratic equation formula, or \"complete the square\" to find the other 2 roots. \n" );
document.write( "

\n" );