Question

Observe the graph of polynomial \(p(x)\). Number of zeroes of \(p(x)\) is

• A. \(5\)
• B. \(4\)
• C. \(6\)
• D. \(3\)

Hint:

Do not count the intersections with the \(y\)-axis. Only intersections with the \(x\)-axis represent the zeroes of \(p(x)\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The number of real zeroes of a polynomial \(y = p(x)\) is the number of times its graph intersects or touches the \(x\)-axis.
Step 3: Detailed Explanation:
Look at the provided graph:
The curve crosses the \(x\)-axis at three distinct points.
1. One point is on the negative \(x\)-axis.
2. One point is at the origin (or very close to it, intersecting the axis).
3. One point is on the positive \(x\)-axis.
Since there are 3 intersection points with the \(x\)-axis, the polynomial has 3 zeroes.
Step 4: Final Answer:
The number of zeroes is \(3\).