Explanation You know that a real number k is a zero of the polynomial p(x) if p(k) = 0. But why are the zeroes of a polynomial so important? To answer this, first we will see the geometrical repres
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Case 1 Here, the graph cuts x-axis at two distinct points A and . The x-coordinates of A and are the two zeroes of the quadratic polynomial ax2 + bx + c in this case (see Fig. 2.3).
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Case 2 Here, the graph cuts the x-axis at exactly one point, i.e., at two coincident points. So, the two points A and of Case (i) coincide here to become one point A (see Fig. 2.4).
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Case 3 Here, the graph is either completely above the x-axis or completely below the x-axis. So, it does not cut the x-axis at any point (see Fig. 2.5). So, the quadratic
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Examples Look at the graphs in Fig. 2.9 given below. Each is the graph of y = p(x), where p(x) is a polynomial. For each of the graphs, find the number of zeroes of p(x). SOLUTION:
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