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

Problem:
The graph of polynomial \(p(x)\) is given.

Objective:
Determine the number of zeroes of \(p(x)\).

Solution:
Zeroes of \(p(x)\) are values of \(x\) where \(p(x) = 0\). Graphically, these are points where the graph intersects the x-axis.

Analyze the graph to find x-intercepts.

The curve crosses the x-axis at three points.
Therefore, the polynomial has 3 distinct zeroes.

Additional Information:
The polynomial's degree is at least equal to the number of zeroes. A polynomial of degree \(n\) has at most \(n\) real zeroes.

Answer:
The number of zeroes is 3.