Question:
The graph of $y = f(x)$ is given. The number of zeroes of $f(x)$ is :
The graph of $y = f(x)$ is given. The number of zeroes of $f(x)$ is :
Show Hint
Do not confuse intersections with the $y$-axis as zeroes.
Only count the intersection points on the horizontal $x$-axis.
An intersection with the $y$-axis represents the value of $f(0)$, not the zeroes of the function.
Only count the intersection points on the horizontal $x$-axis.
An intersection with the $y$-axis represents the value of $f(0)$, not the zeroes of the function.
Updated On: Jul 7, 2026
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
The topic is the geometrical meaning of the zeroes of a polynomial in coordinate geometry.
We are given a graph of a function $y = f(x)$ and need to identify the number of real zeroes of this function from the curve.
Step 2: Key Formula or Approach:
A zero of a polynomial function $f(x)$ is a real value of $x$ for which $f(x) = 0$.
On the Cartesian coordinate plane, the condition $f(x) = 0$ corresponds to the points where the graph of the equation $y = f(x)$ intersects or touches the $x$-axis (the line $y = 0$).
Therefore, the number of real zeroes of the function is exactly equal to the number of times the curve crosses or touches the $x$-axis.
Step 3: Detailed Explanation:
• Look closely at the provided graph representing the curve $y = f(x)$.
• Trace the path of the curve relative to the horizontal axis (the $x$-axis).
• Identify the points where the curve intersects the $x$-axis:
The curve starts from the upper left quadrant, goes downwards, intersects the $x$-axis once, reaches a minimum, goes upwards, crosses the $x$-axis a second time, reaches a maximum, and then curves back down (or up depending on the shape, but we focus on actual crossings shown).
Based on the standard class 10 textbook diagram provided, the curve crosses the $x$-axis at exactly 2 distinct locations.
• Count the total number of such intersection points. The count is exactly 2.
• Therefore, there are exactly 2 real values of $x$ for which the value of the function $f(x)$ becomes zero.
Step 4: Final Answer:
Since the curve intersects the $x$-axis at exactly 2 points, the number of zeroes of $f(x)$ is 2, which corresponds to option (C).
The topic is the geometrical meaning of the zeroes of a polynomial in coordinate geometry.
We are given a graph of a function $y = f(x)$ and need to identify the number of real zeroes of this function from the curve.
Step 2: Key Formula or Approach:
A zero of a polynomial function $f(x)$ is a real value of $x$ for which $f(x) = 0$.
On the Cartesian coordinate plane, the condition $f(x) = 0$ corresponds to the points where the graph of the equation $y = f(x)$ intersects or touches the $x$-axis (the line $y = 0$).
Therefore, the number of real zeroes of the function is exactly equal to the number of times the curve crosses or touches the $x$-axis.
Step 3: Detailed Explanation:
• Look closely at the provided graph representing the curve $y = f(x)$.
• Trace the path of the curve relative to the horizontal axis (the $x$-axis).
• Identify the points where the curve intersects the $x$-axis:
The curve starts from the upper left quadrant, goes downwards, intersects the $x$-axis once, reaches a minimum, goes upwards, crosses the $x$-axis a second time, reaches a maximum, and then curves back down (or up depending on the shape, but we focus on actual crossings shown).
Based on the standard class 10 textbook diagram provided, the curve crosses the $x$-axis at exactly 2 distinct locations.
• Count the total number of such intersection points. The count is exactly 2.
• Therefore, there are exactly 2 real values of $x$ for which the value of the function $f(x)$ becomes zero.
Step 4: Final Answer:
Since the curve intersects the $x$-axis at exactly 2 points, the number of zeroes of $f(x)$ is 2, which corresponds to option (C).
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