NCERT Class 10 Maths • Chapter 2 • Polynomials
Polynomials Class 10 Worksheet with Online Quiz and Games
Connect polynomial graphs with algebra. Use this Polynomials Class 10 worksheet to practise zeroes, coefficient relationships, transformed zeroes and mathematical reasoning.
Attempt an original 20-question online quiz, investigate five interactive polynomial games and solve five HOTS activities. Five additional practice tasks help you check your written methods.
Polynomials Online Quiz for Class 10
Question 1 of 20 • Core reasoning • Answered 0/20
If α and β are the zeroes of 6x² + x − 2, find α² + β².
Polynomials Online Games for Class 10
Explore graphs, construct coefficients, repair an incorrect solution and organise a proof. Each investigation uses a different task from the quiz.
1. Graph Invariance Lab
Change the non-zero multiplier in y = a(x + 4)(x − 2). Investigate whether stretching or reflecting the curve changes its zeroes.
a = 1 y = 1(x + 4)(x − 2)
2. Build a Polynomial
Construct p(x) = 3x² + bx + c with zeroes −5 and 8. Find both missing coefficients.
3. Repair the Sign Error
For 5x² + 15x − 20, a student reports the sum as 3 and the product as −20. Replace both incorrect values.
Student record: sum = 3; product = −20
4. Shift the Zeroes
The zeroes of x² + 2x − 15 are shifted three units to the right. For the new monic polynomial x² + bx + c, find b and c.
5. Build the Coefficient Proof
Arrange the four steps to derive the sum and product relationships. Assume a ≠ 0 and α and β are the zeroes.
Polynomials HOTS Online Activities for Class 10
Investigate a common zero, build a counterexample and connect transformed zeroes with coefficients. Enter your reasoning on paper before checking.
6. Common-Zero Detective
The polynomials x² − 2x − 15 and x² + kx − 30 share a positive zero. Find that common zero and k.
7. Invent a Counterexample
Disprove the claim: “Two pairs of zeroes with the same sum must have the same product.” Enter two integer pairs between −10 and 10.
8. Reciprocal-Zero Constructor
The zeroes of 2x² + 7x + 3 are replaced by their reciprocals. Construct the new polynomial as 3x² + bx + c.
9. Same Zeroes Different Scale
A quadratic has the same zeroes as 3x² − 4x − 7 but leading coefficient −6. Write it as −6x² + bx + c.
10. Design a Touching Graph
Construct p(x) = 2x² + bx + c so its graph touches the x-axis at x = 3. Find b and c.
About This Polynomials Class 10 Worksheet
Read the Class 10 Maths Chapter 2 practice guide
This Polynomials Class 10 worksheet combines printable practice with interactive algebra. Use the existing worksheet download option on this page for written work, then attempt the online questions to identify gaps in your understanding.
In NCERT Class 10 Maths Chapter 2, a zero connects an algebraic expression with its graph: substituting that value makes the polynomial equal to zero. On a graph, look at the x-axis rather than the y-axis. A curve that touches the x-axis also has a real zero at that point.
For quadratic polynomial questions, identify the leading coefficient, the coefficient of x and the constant term with their signs. Use the sum and product of zeroes to verify a factorisation, recover an unknown coefficient or construct a suitable polynomial.
The Polynomials Class 10 online quiz includes non-monic expressions, reciprocal zeroes, parameter questions and graph interpretation. The HOTS activities extend these ideas through counterexamples and transformations. They are original practice questions, not a collection presented as previous year board questions.
A useful written solution explains the method before the final answer. When forming a polynomial, state whether a monic polynomial or a particular leading coefficient is required. Different non-zero constant multiples can have the same zeroes.
Use the linked Polynomials notes and mind map for concept revision. Return to this worksheet for active practice, checking each answer by substitution or by comparing the required sum and product.
Polynomials Class 10 Extra Practice Questions
Complete the calculation in your notebook, enter your answer and check your method.
1. Find and Verify Zeroes
Find the zeroes of x² − 13x + 36. Enter them in increasing order, then verify their sum and product in your notebook.
2. Difference Identity
Two zeroes have sum 9 and product 14. Calculate (α − β)² without finding the zeroes.
3. Find the Parameter
If −6 is a zero of x² + mx + 18, find m.
4. Construct from Two Conditions
Construct the monic polynomial x² + bx + c whose zeroes have sum −5 and product −24.
5. Recover the Constant
For p(x) = x² − 4x + c, you are told p(3) = −2. Find c.
Polynomials Practice Tips for Students
- Arrange the polynomial in descending powers before identifying coefficients.
- Include the negative sign in the sum-of-zeroes formula.
- Divide by the leading coefficient when the polynomial is not monic.
- Check that neither zero is zero before using reciprocals.
- Distinguish two equal zeroes from two distinct x-intercepts.
- For transformed zeroes, calculate their new sum and product first.
- Check a constructed polynomial against every condition in the question.
Tips for Parent and Teacher Support
- Ask the student to explain why a formula applies before substituting numbers.
- Use the graph lab to discuss what changes and what remains invariant.
- Ask for a counterexample when a statement claims something is always true.
- Review the reasoning in incorrect answers before repeating the quiz.
Polynomials Class 10 Worksheet FAQs
How do I find the zeroes of a polynomial?
Find the values of x for which the polynomial equals zero. Factorisation is useful when the expression can be written as a product of simpler factors. Substitute each proposed zero back into the original expression to check it.
What is the relationship between zeroes and coefficients?
For ax² + bx + c with a ≠ 0, the sum of its zeroes is −b divided by a, and their product is c divided by a. Keep the signs of all coefficients when applying these relationships.
How do I form a polynomial from the sum and product of its zeroes?
If the sum is S and the product is P, the monic quadratic polynomial is x² − Sx + P. Multiply the entire expression by the required non-zero leading coefficient when necessary.
How many real zeroes can a quadratic polynomial have?
It can have zero, one or two distinct real zeroes. Use the number of distinct points where its graph meets the x-axis. A touching point counts as one distinct real zero.
Why can different polynomials have the same zeroes?
Multiplying a polynomial by a non-zero constant does not change where it equals zero. However, the graphs can have different heights or opposite orientations.
How do I solve alpha beta questions without finding each zero?
Calculate their sum and product from the coefficients. Rewrite the required expression using these values. For example, α² + β² equals (α + β)² − 2αβ.
How do I find a missing coefficient when one zero is given?
Substitute the given zero into the polynomial and equate the result to zero. Solve the resulting equation for the missing coefficient, then check the original condition.
What changes when the zeroes are replaced by their reciprocals?
Both original zeroes must be non-zero. The new sum is the original sum divided by the original product. The new product is the reciprocal of the original product.
Which Polynomials Class 10 questions should I practise?
Include graph interpretation, finding and verifying zeroes, unknown coefficients, polynomial construction and alpha beta identities. Add reasoning questions that ask you to justify, compare or disprove a claim.
Does this worksheet include answers and explanations?
The online quiz shows explanations after submission. Each interactive activity and extra practice task provides feedback when you check your answer. Use the printable worksheet alongside this online practice.
Practise with the Polynomials Online Quiz for Class 10
Revisit the questions you found difficult, explain the coefficient relationships in your own words and try the quiz again after completing the investigations.
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