Question

how many complex roots does the function $y = x^3 - 2x + 3$ have?

a. 0

b. 1

c. 2

d. 3

Explanation:

Step1: Recall the Fundamental Theorem of Algebra

A polynomial of degree \( n \) has exactly \( n \) complex roots (counting multiplicities). The given function is \( y = x^3 - 2x + 3 \), which is a cubic polynomial (degree 3).

Step2: Determine the number of complex roots

By the Fundamental Theorem of Algebra, a cubic polynomial (degree 3) has 3 complex roots (since complex roots include real roots, and non - real complex roots come in conjugate pairs, but the total number of complex roots (counting multiplicities) for a degree \( n \) polynomial is \( n \)).

Answer:

D. 3