Polynomials — Class 10 Maths MCQ with Answers (2026-27)

Updated 23 August 2026 · checked against the CBSE 2026-27 syllabus

13 objective questions on Polynomials, every one checked against the CBSE 2026-27 syllabus. Pick an option and the correct answer is shown straight away, with your marks running at the top. A new question opens each day until all 13 are unlocked.

Polynomials MCQ questions with answers

1. In the standard form of quadratic polynomial ax² + bx + c,‌​ a, b and c are
   1. All are real numbers
   2. All are rational numbers
   3. 'a' is a non-zero real number and b and c are any real numbers
   4. All are integers

   Answer: c) 'a' is a non-zero real number and b and c are any real numbers

   A quadratic needs the x² term to survive, so a cannot be 0. There is no requirement for b and c beyond being real.

2. If α and 1/α are the zeroes of the quadratic polynomial 2x²​‌ − x + 8k, then k is
   1. 4
   2. ¼
   3. −¼
   4. 2

   Answer: b) ¼

   Product of zeroes = c/a = 8k/2 = 4k. Here the zeroes are α and 1/α, whose product is 1. So 4k = 1 and k = ¼.

3. The graph of x² + 1‌‌ = 0
   1. Intersects x-axis at two distinct points
   2. Touches x-axis at a point
   3. Neither touches nor intersects x-axis
   4. Either touches or intersects x-axis

   Answer: c) Neither touches nor intersects x-axis

   x² + 1 = 0 gives x² = −1, which no real number satisfies. With no real zeroes the graph never meets the x-axis.

4. If the sum of the roots is −p and product of​​ the roots is −1/p, then the quadratic polynomial is
   1. k(−px² + x/p + 1)
   2. k(px² − x/p − 1)
   3. k(x² + px − 1/p)
   4. k(x² − px + 1/p)

   Answer: c) k(x² + px − 1/p)

   A quadratic with known zeroes is k[x² − (sum)x + product]. Substituting sum = −p and product = −1/p gives k(x² + px − 1/p).

5. An asana is a body posture. In the figure, one can observe that the poses can be related to the representation of a quadratic‌​ polynomial. The shape of the poses shown is
   1. Spiral
   2. Ellipse
   3. Linear
   4. Parabola

   Answer: d) Parabola

   A quadratic polynomial always graphs as a parabola — a single smooth U-shaped curve, which is the shape the poses trace.

6. The graph of a parabola opens downwards,‌ if‌ ______
   1. a ≥ 0
   2. a = 0
   3. a < 0
   4. a > 0

   Answer: c) a < 0

   The sign of a decides the opening direction. A negative leading coefficient turns the parabola downwards.

7. Refer to the figure in your textbook or question paper.

   *(Figure required: a parabola cutting the x-axis at −2 and 4, vertex near​ (1,​ −9).)* In the graph, how many zeroes are there for the polynomial?
   1. 0
   2. 1
   3. 2
   4. 3

   Answer: c) 2

   The zeroes are where the curve crosses the x-axis. This parabola crosses at two points, so it has 2 zeroes.

8. The two zeroes in‌ the​ above shown graph are
   1. 2, 4
   2. −2, 4
   3. −8, 4
   4. 2, −8

   Answer: b) −2, 4

   Read off the x-coordinates of the two crossing points: x = −2 and x = 4.

9. The zeroes of the quadratic​ polynomial‌ 4√3x² + 5x − 2√3 are
   1. 2/√3, √3/4
   2. −2/√3, √3/4
   3. 2/√3, −√3/4
   4. −2/√3, −√3/4

   Answer: b) −2/√3, √3/4

   Split the middle term: 4√3x² + 8x − 3x − 2√3 = 4x(√3x + 2) − √3(√3x + 2). Setting each factor to zero gives x = −2/√3 and x = √3/4.

10. If the sum of the zeroes of the quadratic polynomial 5x² – kx + 7 is 4,​ then​ find the value of k.
    1. 20
    2. 21
    3. 18
    4. 19

    Answer: a) 20

    Sum of zeroes = −b/a = k/5. Setting k/5 = 4 gives k = 20.

11. If α and β are the zeroes of a polynomial‌ x²​ − 4√3x + 3, then find the value of α + β − αβ.
    1. 4√3
    2. −3
    3. 4√3 − 3
    4. −4√3 − 3

    Answer: c) 4√3 − 3

    Sum of zeroes = 4√3 and product = 3. So α + β − αβ = 4√3 − 3.

12. What is the quadratic polynomial whose‌ sum‌ and product of zeroes are √2 and ⅓ respectively?
    1. 3x² − 3√2x + 1
    2. 3x² + 3√2x + 1
    3. 2x² + 3√2x − 1
    4. 2x² + 3√2x − 1

    Answer: a) 3x² − 3√2x + 1

    Use k[x² − (sum)x + product] = x² − √2x + ⅓. Multiplying through by 3 clears the fraction: 3x² − 3√2x + 1.

13. A quadratic polynomial has integral roots. The sum of its roots is 7.​ Which​ of the following cannot be the constant term of the polynomial?
    1. 6
    2. 10
    3. 12
    4. 14

    Answer: d) 14

    List integer pairs summing to 7 and take their products: (1,6)→6, (2,5)→10, (3,4)→12, (0,7)→0. No integer pair gives 14, so 14 is impossible.