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NCERT Class 10 Mathematics – Chapter 2: Polynomials
Board Exam 2026 focused online test based strictly on NCERT textbook.
- A polynomial can have one or more terms.
- Degree of a polynomial is the highest power of the variable.
- Zeroes of a polynomial are the x-values where the polynomial equals zero.
- The number of zeroes equals the number of intersections with the x-axis.
- There is a relationship between zeroes and coefficients.
Q1. The degree of the polynomial 5x³ + 4x² − 7 is:
1
3
2
0
The highest power of x is 3.
Q2. A polynomial of degree zero is called:
Constant polynomial
Linear polynomial
Quadratic polynomial
Cubic polynomial
Degree zero corresponds to a constant.
Q3. Which of the following is a quadratic polynomial?
2x + 1
5
x² − 3x + 2
3x³ − 1
The highest power is 2.
Q4. Number of zeroes of a polynomial equals the number of:
Terms
Variables
Coefficients
Points where the graph cuts the x-axis
Graphical interpretation from NCERT.
Q5. Zero of the polynomial p(x)=x−5 is:
5
−5
0
1
x−5=0 ⇒ x=5.
Q6. A linear polynomial has degree:
0
1
2
3
Linear means degree 1.
Q7. The graph of a linear polynomial is a:
Curve
Circle
Straight line
Parabola
Linear graphs are straight lines.
Q8. A quadratic polynomial can have at most:
1 zero
0 zeroes
3 zeroes
2 zeroes
Degree 2 ⇒ at most 2 zeroes.
Q9. The number of zeroes of a non-zero constant polynomial is:
1
0
2
Infinite
A non-zero constant never equals zero.
Q10. Which of the following is a cubic polynomial?
x³ + x + 1
x² + 1
2x + 3
5
Highest power is 3.
Q11. The zero of p(x)=2x+6 is:
−6
−3
3
6
2x+6=0 ⇒ x=−3.
Q12. Degree of 7x²−x+9 is:
1
0
2
3
Highest power is 2.
Q13. A polynomial of degree 1 has graph of:
Parabola
Circle
Ellipse
Straight line
Linear polynomial graph.
Q14. Number of zeroes of x²−4 is:
2
1
0
3
x²−4=(x−2)(x+2).
Q15. The polynomial with zeroes 2 and −3 is:
x²+x−6
x²+x−6
x²−x−6
x²−5
(x−2)(x+3)=x²+x−6.
Q16. The degree of constant zero polynomial is:
0
1
Not defined
2
Zero polynomial has no defined degree.
Q17. Which polynomial has exactly one zero?
x²+1
x²−4
x²
x+5
Linear polynomial has one zero.
Q18. The number of zeroes of x²+1 is:
2
0
1
Infinite
No real roots.
Q19. If α and β are zeroes of x²−5x+6, then α+β is:
5
−5
6
−6
Sum = coefficient relation.
Q20. If α and β are zeroes of x²−5x+6, then αβ is:
−6
−5
6
5
Product = constant term.
Q21. Number of zeroes of x³−x is:
1
3
2
0
x(x−1)(x+1).
Q22. The polynomial x² has zero at:
0
1
−1
2
x²=0 ⇒ x=0.
Q23. The graph of quadratic polynomial is:
Line
Circle
Ellipse
Parabola
Quadratic graphs are parabolas.
Q24. Which of the following is not a polynomial?
3x²
5
1/x
x−1
Negative power not allowed.
Q25. The polynomial whose graph cuts x-axis at exactly one point is:
x²+1
x+2
x²−1
x³−x
Linear graph cuts once.
Q26. The value of k for which x−k has zero at 3 is:
3
−3
0
1
x−k=0 at x=3 ⇒ k=3.
Q27. Which polynomial has degree 4?
x³
x²
x
x⁴−1
Highest power 4.
Q28. The number of zeroes of x³ is:
3
1
0
2
x³=0 ⇒ x=0.
Q29. If sum of zeroes is 0 and product is −1, polynomial is:
x²+1
x²−1
x²−1
x²+1
Standard relation.
Q30. A polynomial of degree n can have at most:
n zeroes
n+1 zeroes
2n zeroes
Infinite zeroes
NCERT theorem.
Q31. The number of zeroes of x²+4x+4 is:
2
1
0
3
(x+2)².
Q32. Which of the following has no real zero?
x²−9
x²
x²−4
x²+1
Always positive.
Q33. The polynomial x²−3x+2 has zeroes:
1 and 3
−1 and −2
1 and 2
2 and 3
(x−1)(x−2).
Q34. Which of the following is a monomial?
7x²
x+1
x²−1
x³+x
Single term.
Q35. The number of terms in 3x²−2x+5 is:
2
3
1
4
Three terms.
Q36. The coefficient of x in 4x²+7x−1 is:
4
−1
7
2
Coefficient is 7.
Q37. Which polynomial has exactly two zeroes?
x
5
x³
x²−1
Quadratic with two roots.
Q38. The degree of polynomial 9 is:
0
1
2
Not defined
Constant non-zero.
Q39. If p(x)=x²−4x+4, then p(2) equals:
4
0
2
−4
p(2)=0.
Q40. The graph of x² cuts x-axis at:
Two points
No point
One point
Three points
Touches at origin.
Q41. The polynomial whose zeroes are −2 and 3 is:
x²+1
x²+5x+6
x²−x−6
x²−x−6
(x+2)(x−3).
Q42. The number of zeroes of x²+2x+1 is:
1
2
0
3
Perfect square.
Q43. The polynomial which has no term independent of x is:
x+1
x
x²+1
5
No constant term.
Q44. Which of the following is a binomial?
x
5
x+1
x²+x+1
Two terms.
Q45. The degree of 3x²y + 2y² is:
1
2
3
Not in one variable
Not single-variable polynomial.
Q46. A polynomial in one variable has:
Only one variable
Two variables
Three variables
No variables
Definition.
Q47. The number of zeroes of a linear polynomial is:
0
1
2
Infinite
Degree 1.
Q48. The value of k if x−k has zero −2 is:
2
0
−2
1
x−k=0 at x=−2.
Q49. Which polynomial has exactly three zeroes?
x
x²
x²−1
x³
Degree 3.
Q50. Polynomials are studied in NCERT primarily to understand:
Only graphs
Algebraic expressions and their zeroes
Geometry
Statistics
Core NCERT objective.
📘 NCERT Class 10 Maths – Chapter-wise Online Tests
- Chapter 1: Real Numbers – Online Test
- Chapter 2: Polynomials – Online Test
- Chapter 3: Pair of Linear Equations in Two Variables – Online Test
- Chapter 4: Quadratic Equations – Online Test
- Chapter 5: Arithmetic Progressions – Online Test
- Chapter 6: Triangles – Online Test
- Chapter 7: Coordinate Geometry – Online Test
- Chapter 8: Introduction to Trigonometry – Online Test
- Chapter 9: Applications of Trigonometry – Online Test
- Chapter 10: Circles – Online Test
- Chapter 11: Areas Related to Circles – Online Test
- Chapter 12: Surface Areas and Volumes – Online Test
- Chapter 13: Statistics – Online Test
- Chapter 14: Probability – Online Test
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