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?

According to the fundamental theorem of algebra, a polynomial has the number of zeros equivalent to the degree of the polynomial.

A quadratic equation is of degree 2 and hence has 2 zeros.

A complex zero is of the form which represents two zeros: a + bi and a - bi.

Thus, since a quadratic equation has only 2 zeros, a quadratic equation with a complex zero already have two zeros and hence will not have any other zero.

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