- The graph of is given. The number of zeroes of is : (a) 0 (b) 1 (c) 2 (d) 4
- The graph of is given. The number of zeroes of is : (a) 0 (b) 1 (c) 2 (d) 4
Options
Official answer
(c) 2 — the graph cuts the x-axis at exactly two points, so has 2 zeroes.
Marking scheme
- 1.1 mark: correct option (c) 2, based on the graph cutting the x-axis at two points.
- 2.Acceptable if a differently-printed figure clearly shows a different number of x-axis intersections; the marking follows the actual crossings shown.
Hint
Count the number of points where the curve meets (cuts or touches) the x-axis — that is the number of zeroes.
Quick oral answer
The number of zeroes is the number of points where the graph meets the x-axis; here it crosses at two points, so has 2 zeroes.
Common mistakes
- 1.Counting where the curve meets the y-axis instead of the x-axis — zeroes correspond only to x-axis intersections.
- 2.Counting the number of turning points (peaks/valleys) rather than x-axis crossings.
- 3.Assuming the number of zeroes equals the degree without actually looking at how many times the graph meets the x-axis.
Analysis and explanation
This MCQ tests the geometrical meaning of zeroes of a polynomial from its graph.
Concept
- The number of zeroes of equals the number of points where the graph cuts or touches the x-axis.
Key points
- The given curve meets the x-axis at 2 distinct points, so has 2 zeroes.
- 0 zeroes would mean the graph never touches the axis; 1 would mean a single touch/cut; 4 would need four crossings.
Common mistakes
- Counting the number of "humps" in the curve instead of actual x-axis intersections.
- Note: the exact count depends on the printed figure — always count the actual crossings shown.
Interesting facts
A polynomial of degree n can have AT MOST n real zeroes, so it can cut the x-axis at most n times — but it may have fewer if some zeroes are complex or repeated.
When a graph just TOUCHES the x-axis and turns back (does not cross), that point is a repeated (double) zero — it counts once as a location but represents two equal roots.
The idea of reading zeroes off a graph connects algebra to coordinate geometry, a link formalised by René Descartes in the 17th century through the Cartesian plane.
Question details
Q4 of 53 questions
- Board
- CBSE
- Class
- Class 10
- Subject
- Mathematics (Basic)
- Year
- 2026
- Section
- Section A
- Marks
- 1
- Type
- MCQ
- Chapter
- Polynomials
- Topic
- Number of zeroes from graph
- Bloom's level
- analyze
- Syllabus topic
- Unit 2: Algebra — Polynomials: Geometrical Meaning of the Zeroes of a Polynomial
- Author
- CBSE
- Reviewed by
- Padhantu Academic Team
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Frequently asked questions
How do you find the number of zeroes of a polynomial from its graph?
Count the number of distinct points where the graph of cuts or touches the x-axis. Each such point is a zero, so the number of x-axis intersections equals the number of real zeroes.
Does a graph touching the x-axis count as a zero?
Yes. A point where the curve touches the x-axis and turns back is a repeated (double) zero. It is one location on the graph but corresponds to two equal roots of the polynomial.
Why is the answer here 2 and not 4?
The shown curve meets the x-axis at only two points. For the answer to be 4, the graph would have to cross the x-axis at four separate points. Since only two crossings are visible, has 2 zeroes.