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Answer:
b. intersects x-axis
Step-by-step explanation:
A zero of the polynomial is where y = 0. The equation y = 0 is the equation of the x-axis, so intersections of the graph of the function with the x-axis are places where the function value is zero.
The number of (distinct real) zeros is equal to the number of points where the graph intersects the x-axis.
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Additional comment
When (x -p)^n is a factor of the polynomial, the graph will intersect the x-axis at x=p. The zero is said to have "multiplicity n". For odd values of n, the graph will cross the x-axis (change sign) at x=p. For even values of n, the graph will touch the axis at x=p, but will not cross there.
So, the number of intersections with the x-axis tells the number of distinct real zeros, but does not say anything about their multiplicity. Complex zeros will not cause the graph to touch the x-axis.
