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Answer:
Part A: There are 4 zeros of the polynomial function f(x)
Part B: The zeroes of the polynomial function f(x) are -4, -1, 0, 2 ⇒ C
Step-by-step explanation:
<em>The zeroes of a function are </em><em>the x-coordinates of the point of intersection between the graph of the function and the x-axis</em><em> (x-intercepts) which means </em><em>values of x at y = 0</em>
Part A:
In the given graph
∵ The graph of the function f(x) = - - 3x³ + 6x² + 8x intersects the x-axis
at 4 points
→ That means there are 4 values of x have y = 0
∴ The number of zeroes of the function is 4
∴ There are 4 zeros of the polynomial function f(x)
Part B:
∵ The graph intersects the x-axis at points (-4, 0), (-1, 0), (0, 0), (2, 0)
→ That means the values of x at y = 0 are -4, -1, 0, 2
∴ f(x) = 0 at x = -4, -1, 0, 2
∴ The zeroes of the polynomial function f(x) are -4, -1, 0, 2