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Class 10 Polynomials: 8 practice questions with answers, step by step
These are 8 practice questions on NCERT Class 10 Maths Chapter 2, Polynomials, each with a worked answer. They cover what the chapter asks: finding the zeroes of a quadratic, using the sum and product of zeroes, finding an unknown coefficient, and reading zeroes from a graph. Try each one on paper before you open the answer.
These questions are our own, drafted with AI help. Every answer was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.
What the chapter says you need
Five facts from the NCERT textbook (Mathematics, Textbook for Class X, Reprint 2026-27, Chapter 2, printed pages 10 to 23) cover every question below:
- A real number k is a zero of a polynomial p(x) if p(k) = 0 (section 2.1, page 11).
- The zeroes of p(x) are the x-coordinates of the points where the graph of y = p(x) meets the x-axis (section 2.2, page 12, and the summary, page 23).
- A quadratic polynomial has at most 2 zeroes and a cubic polynomial has at most 3 (page 17 and the summary, page 23).
- If α and β are the zeroes of ax² + bx + c, then α + β = −b/a and αβ = c/a (section 2.3, pages 19 and 20; summary, page 23).
- To find the zeroes of a quadratic, split the middle term and put each factor equal to zero, as in the textbook's examples on page 19.
Zeroes, and their sum and product
Question 1. α and β are the zeroes of x² − 7x + 12. Find α + β.
Answer: Sum of zeroes = −b/a = −(−7)/1 = 7. (Check: the zeroes are 3 and 4, and 3 + 4 = 7.)
Question 2. For the same polynomial x² − 7x + 12, find αβ.
Answer: Product of zeroes = c/a = 12/1 = 12. (Check: 3 × 4 = 12.)
Question 3. What is the larger zero of x² − 5x + 6?
Answer: x² − 5x + 6 = (x − 2)(x − 3), so the zeroes are 2 and 3. The larger is 3.
Question 4. Find the sum of the zeroes of 3x² − 12x + 5.
Answer: Sum of zeroes = −b/a = −(−12)/3 = 4. You do not need to find the zeroes themselves to answer this.
Unknown coefficients and checking a zero
Question 5. One zero of x² + kx − 10 is 2. Find k.
Answer: A zero makes the polynomial 0, so put x = 2: 4 + 2k − 10 = 0, so 2k = 6 and k = 3. Check: x² + 3x − 10 = (x − 2)(x + 5), which has the zero 2.
Question 6. Check that −2 and 5 are zeroes of p(x) = x² − 3x − 10.
Answer: p(−2) = 4 + 6 − 10 = 0 and p(5) = 25 − 15 − 10 = 0. Both values are 0, so −2 and 5 are zeroes. Check with the formulas: the sum of zeroes is −2 + 5 = 3 = −(−3)/1, and the product is −10 = c/a.
Counting zeroes and reading a graph
Question 7. What is the greatest number of zeroes a cubic polynomial can have?
Answer: 3. A cubic polynomial can have at most three zeroes (it may have fewer). The textbook shows this with the graphs of cubic polynomials on page 17.
Question 8. The graph of y = p(x) meets the x-axis at the points (−3, 0) and (4, 0) and nowhere else. What are the zeroes of p(x)?
Answer: −3 and 4. The zeroes of a polynomial are the x-coordinates of the points where its graph meets the x-axis. (Page 12 and summary, page 23.)
Practise more, and check your marks
- Free practice, marked instantly in your browser: Class 10 Polynomials questions. Questions 1 to 5 above are all in this set.
- Printable worksheets with answer keys, in English, Hindi and Marathi: Class 10 worksheets.
- See which unit this chapter belongs to and how CBSE splits the 80 theory marks in our Class 10 Maths syllabus 2026-27 guide.
- The same step-by-step style for the next chapters: Class 10 Pair of Linear Equations and Class 10 Quadratic Equations.
Where CMDLearn fits
CMDLearn is building an AI tutor for Classes 1 to 10 that explains a step and checks the child's working, but leaves the writing to the child. It is still in development, and no child uses it yet. If you would like to hear when there is something to try, you can join the waitlist.
Sources
All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook.
- NCERT, Mathematics, Textbook for Class X, Chapter 2 "Polynomials" (Reprint 2026-27), printed pages 10-23 (zero of a polynomial, section 2.1, page 11; zeroes and the graph, section 2.2, page 12; at most 3 zeroes for a cubic, page 17; the sum and product of the zeroes of a quadratic, section 2.3, pages 19-20; summary, page 23): ncert.nic.in/textbook/pdf/jemh102.pdf
The definitions and relationships are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the official CBSE notices.