第 10 类 NCERT 解决方案 - 第 2 章多项式 - 练习 2.1

问题 1. 对于一些多项式 p(x)，y = p(x) 的图如下图 2.10 所示。在每种情况下，找出 p(x) 的零点数。

解决方案：

So, we have equation y = p(x). When p(x) = 0, y = 0. 

That means we only need to find the number of times we get y = 0 in the graph.

In other words, the number of times the graph intersects the x-axis is the answer.

(i) 0. Because the graph doesn’t intersect the x-axis.

(ii) 1. Because the graph intersects the x-axis only at one point.

(iii) 3. Because the graph intersects the x-axis at three points.

(iv) 2. Because the graph intersects the x-axis at two points.

(v) 4. Because the graph intersects the x-axis at four points.

(vi) 3. Because the graph intersects the x-axis at three points.