document.write( "Question 1210413: Find a degree 3 polynomial with real coefficients having zeros 1 and 4i and a lead coefficient of 1. Write P in expanded form. Be sure to write the full equation, including P(x) =. \n" ); document.write( "

Algebra.Com's Answer #852347 by ikleyn(52957) $\"\"$ $\"About$

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\n" ); document.write( "Find a degree 3 polynomial with real coefficients having zeros 1 and 4i and a lead coefficient of 1.
\n" ); document.write( "Write P in expanded form. Be sure to write the full equation, including P(x) =.
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document.write( "If a polynomial with real coefficients has a root which is a complex number, \r\n" );
document.write( "then this polynomial has another root which is the conjugate complex number.\r\n" );
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document.write( "It is a general property of polynomials with real coefficients.  \r\n" );
document.write( "In our case, it means that the seeking polynomial has the roots  4i,  -4i  and  1.\r\n" );
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document.write( "Hence, the seeking polynomial is\r\n" );
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document.write( "    P(x) = (x-1)*(x-4i)*(x-(-4i)) = (x-1)*(x^2+16) = x^3 - x^2 + 16x - 16.\r\n" );
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document.write( "ANSWER.  P(x) = x^3 - x^2 + 16x - 16.\r\n" );
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