Write the number of rational and irrational zeros of the given cubic function. X³ - 2 A)Rational zeros: 1;irrational zeros: 0 B)Rational zeros: 1;irrational zeros: 2 C)Rational zeros: 1;irrational zeros: 1 D)Rational zeros: 0;irrational zeros: 1 E)Rational zeros: 0;irrational zeros: 0

Question

Quizplus · Accepted Answer

The given cubic function has no rational roots. By the rational root theorem, if the polynomial has any rational roots, they must be factors of the constant term (in this case, -2) divided by a factor of the leading coefficient (which is 1). However, -2 has no rational factors. Therefore, the only possible zeros are irrational, and there is only one such zero by the fundamental theorem of algebra.

Write the Number of Rational and Irrational Zeros of the Given