You know that polynomial equations can have real or complex zeros. Suppose the quadratic equation has one complex zero. According to the Fundamental Theorem of Algebra, does this equation have any other zeros? If so, how many zeros does it have?

Question

You know that polynomial equations can have real or complex zeros. Suppose the quadratic equation   has one complex zero. According to the Fundamental Theorem of Algebra, does this equation have any other zeros? If so, how many zeros does it have?

princessaurora · Answer

*I forgot to put the equation* It's ax^2+bx+c=0

directrix · Answer

The set of Real numbers is a subset of the set of Complex numbers. I don't know why this question is distinguishing between the two.

The quadratic will have two zeros according to the theorem you cited.

The zero may be a double as in the case or y = x^2 where the zeros are 0 and 0.

If by complex root, the question means that  you know 2 + 3i is a zero, then 2 - 3i is also a zero. 

With the theorem, you always have to account for a number of roots which is the same as the degree of the polynomial.  

In this case, ax^2+bx+c=0, you have to account for two zeros.