## 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.