Question

What can you say about the nature of any other zeros of the quadratic equation , which has one complex zero? Explain your answer.

Answer 1

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 $a\pm bi$ 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.