document.write( "Question 650721: If f(x) is a polynomial function of degree greater than 2, and f(x) has only one zero, then can you say whether the zero is real or complex?\r
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Algebra.Com's Answer #852481 by ikleyn(53153) $\"\"$ $\"About$

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\n" ); document.write( "If f(x) is a polynomial function of degree greater than 2, and f(x) has only one zero,
\n" ); document.write( "then can you say whether the zero is real or complex?
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document.write( "As the problem is worded, it only makes sense, when the coefficients of the polynomial\r\n" );
document.write( "are real numbers (the condition which is omitted in the problem).\r\n" );
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document.write( "    It is because if the polynomial has complex number coefficients, then\r\n" );
document.write( "    the set of the roots must be considered over complex numbers, and in\r\n" );
document.write( "    this case the number of roots is equal to the degree of the polynomial,\r\n" );
document.write( "    which in this problem is greater than 2.\r\n" );
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document.write( "OK.  But then, if the existing root is a complex number, then there is another complex root number\r\n" );
document.write( "     different from the first one and conjugated with the first complex number root.\r\n" );
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document.write( "     But because we are given that f(x) has only one root, it means that the existing single \r\n" );
document.write( "     root is a real number.\r\n" );
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