Question 650721
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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?
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<pre>
As the problem is worded, it only makes sense, when the coefficients of the polynomial
are real numbers (the condition which is omitted in the problem).


    It is because if the polynomial has complex number coefficients, then
    the set of the roots must be considered over complex numbers, and in
    this case the number of roots is equal to the degree of the polynomial,
    which in this problem is greater than 2.


OK.  But then, if the existing root is a complex number, then there is another complex root number
     different from the first one and conjugated with the first complex number root.

     But because we are given that f(x) has only one root, it means that the existing single 
     root is a real number.
</pre>

Solved and explained.