Question

In the given figure, graph of polynomial \(p(x)\) is shown. Number of zeroes of \(p(x)\) is

• A. 3
• B. 2
• C. 1
• D. 4

Hint:

The number of zeroes of a polynomial equals the number of times its graph crosses the x-axis.

Answer 1

The Correct Option is A

Given:
The graph of polynomial \(p(x)\) is provided.

To find:
The number of zeroes of the polynomial \(p(x)\).

Step 1: Understand what zeroes of a polynomial are
Zeroes of a polynomial \(p(x)\) are the values of \(x\) for which \(p(x) = 0\).
Graphically, these correspond to the points where the graph of the polynomial touches or crosses the x-axis.

Step 2: Analyze the graph
Look at the points where the curve intersects the x-axis.
Each point where the curve crosses or touches the x-axis corresponds to a root (zero) of the polynomial.

Step 3: Count the number of x-intercepts
From the graph, observe:
- The curve crosses the x-axis three times.
- Hence, the polynomial has 3 distinct zeroes.

Additional note:
- The degree of the polynomial is at least equal to the number of zeroes.
- If the polynomial is of degree \(n\), it can have at most \(n\) real zeroes.

Final Answer:
The number of zeroes of the polynomial \(p(x)\) is 3.