Question

how many real zero(s) exist for the polynomial? f(x)=-x⁴ -x³ + 3x² - 3

Explanation:

Step1: Identify x-axis intersections

A real zero of a polynomial corresponds to where its graph crosses or touches the x-axis ($y=0$).

Step2: Analyze the given graph

The provided graph of $f(x)=-x^4 - x^3 + 3x^2 - 3$ never intersects or touches the x-axis (all points on the graph have $y$-values either positive or negative, but never 0).

Step3: Count real zeros

Since there are no x-axis intersections, the number of real zeros is 0.

Answer:

0