Question

According to the Fundamental Theorem of Algebra, how many zeros does the function

f(x)=2x−3x^4−5x^2+9x^3−10x+7 have?

A. 2

B. 3

C. 4

D. 5

Answer 1

The function f(x) is a fourth-degree polynomial, and by the Fundamental Theorem of Algebra, it will have exactly 4 zeros.

Step-by-step explanation:

According to the Fundamental Theorem of Algebra, every non-zero, single-variable, degree n polynomial with complex coefficients has exactly n zeros (including multiplicity). The given function f(x) = 2x−3x4−5x2+9x3−10x+7 is a fourth-degree polynomial, as indicated by its highest power of x, which is 4. Therefore, this polynomial will have exactly 4 zeros.