document.write( "Question 1028848: Find a 3rd degree polynomial with roots 6 and -i with constant coefficient -24.\r
\n" ); document.write( "\n" ); document.write( "A. f(x)=4x^3-24x^2+24x-24
\n" ); document.write( "B. f(x)=4x^3-24x^2+4x-24
\n" ); document.write( "C. f(x)=x^3-6x^2+x-24
\n" ); document.write( "D. f(x)=-4x^3+24x^2+4x-24
\n" ); document.write( "E. None of the above \n" ); document.write( "

Algebra.Com's Answer #643902 by ikleyn(52810) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Find a 3rd degree polynomial with roots 6 and -i with constant coefficient -24.\r
\n" ); document.write( "\n" ); document.write( "A. f(x)=4x^3-24x^2+24x-24
\n" ); document.write( "B. f(x)=4x^3-24x^2+4x-24
\n" ); document.write( "C. f(x)=x^3-6x^2+x-24
\n" ); document.write( "D. f(x)=-4x^3+24x^2+4x-24
\n" ); document.write( "E. None of the above
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Under the given conditions, the roots of the polynomial should be 6, +i and -i.\r\n" );
document.write( "\r\n" );
document.write( "Let us check the polynomial B.\r\n" );
document.write( "\r\n" );
document.write( "f(x) =  =  +  = \r\n" );
document.write( "\r\n" );
document.write( "=  +  = .\r\n" );
document.write( "\r\n" );
document.write( "Now you can see that this factored polynomial satisfies to the given condition.\r\n" );
document.write( "\r\n" );
document.write( "So, the option B is good.\r\n" );
document.write( "\r\n" );
document.write( "For the polynomials A) and C) the number 6 is not the root.\r\n" );
document.write( "\r\n" );
document.write( "For the polynomial  D)        the number i is not the root.\r\n" );
document.write( "\r\n" );
document.write( "So, the answer is the only option B.\r\n" );
document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );