Question

The graph of a polynomial intersects the y-axis at one point and the x-axis at two points. The number of zeroes of this polynomial are :

• A. 1
• B. 2
• C. 3
• D. 0

Answer 1

The Correct Option is B

Step 1: Understand the given situation:
We are given that the graph of a polynomial intersects the y-axis at one point and the x-axis at two points. The task is to determine the number of zeroes of the polynomial.

Step 2: Understand the significance of the y-axis and x-axis intersections:
- The graph of the polynomial intersects the y-axis at one point. The y-axis intersection corresponds to the value of the polynomial at \( x = 0 \), which is the constant term of the polynomial. This means the polynomial has a defined value at \( x = 0 \).
- The graph intersects the x-axis at two points. Each intersection with the x-axis corresponds to a zero of the polynomial (i.e., a value of \( x \) for which the polynomial evaluates to zero). Hence, the polynomial has two distinct zeroes.

Step 3: Relate the number of x-axis intersections to the number of zeroes:
- If a polynomial intersects the x-axis at two distinct points, it has two real zeroes at those points.
- The number of zeroes of a polynomial is equal to its degree. Since the graph intersects the x-axis at two distinct points, the degree of the polynomial is at least 2, and since it is specified to intersect the x-axis exactly at two points, the polynomial has exactly two zeroes.

Step 4: Conclusion:
Since the graph intersects the x-axis at two points, the polynomial has exactly two zeroes. Therefore, the correct answer is \( \boxed{2} \).