Chapter 2 Ex.2.1 Question 1
The graphs of \(y{ }={ }p\left( x \right)\) are given in the figure below, for some polynomials \(p\left( x \right)\). Find the number of zeroes of \(p\left( x \right)\) in each case.

What is known?
The graphs of \(y{ }={ }p\left( x \right)\) are given in the above figure for some polynomials \(p\left( x \right)\).
What is unknown?
The number of zeroes of \(p\left( x \right)\) in each case.
Reasoning:
You can reach the solution easily by understanding the statement of the question. As The graphs of \(y{ }={ }p\left( x \right)\) are given and you have to find the number of zeroes of \(p\left( x \right)\) in each case.
To find this look at the graphs and visually find how many points it cuts the \(x\)-axis. The number of points the graph cuts or touches the \(x\)-axis. The number of points it cut or touches the \(x\)-axis are the zeroes of the polynomial \(p\left( x \right)\).
Steps:
(i) The number of zeroes is \(0\) as the graph doesn’t cuts the \(x\)-axis at any point.
(ii) The number of zeroes is \(1\) as the graph cuts the \(x\)-axis at only one point.
(iii) The number of zeroes is \(3\) as the graph cuts the \(x\)-axis at \(3\) points.
(iv) The number of zeroes is \(2\) as the graph cuts the \(x\)-axis at \(2\) points.
(v) The number of zeroes is \(4\) as the graph cuts the \(x\)-axis at \(4\) points.
(vi) The number of zeroes is \(3\) as the graph cuts the \(x\)-axis at \(3 \) points.