Exercise 2.1 • Q1
The graphs of y = p(x) are given in the following figures for some polynomials p(x). Find the number of zeroes of p(x), in each case.
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Key Concept
The number of zeroes of the polynomial p(x) is equal to the number of points where the graph intersects the X-axis.
(i) Graph 1
The graph represents a line parallel to the X-axis. It does not intersect the X-axis at any point.
Answer: No zeroes (0).
Answer: No zeroes (0).
(ii) Graph 2
The graph intersects the X-axis at one point.
Answer: 1 Zero.
Answer: 1 Zero.
(iii) Graph 3
The graph intersects the X-axis at three points.
Answer: 3 Zeroes.
Answer: 3 Zeroes.
(iv) Graph 4
The graph (a parabola) intersects the X-axis at two points.
Answer: 2 Zeroes.
Answer: 2 Zeroes.
(v) Graph 5
The graph intersects the X-axis at four points.
Answer: 4 Zeroes.
Answer: 4 Zeroes.
(vi) Graph 6
The graph intersects the X-axis at one distinct point and touches the X-axis at two points. Since touching counts as an intersection point for zeroes:
Total points of contact = 3.
Answer: 3 Zeroes.
Total points of contact = 3.
Answer: 3 Zeroes.