CBSE BOARD PYQS · CHAPTER 02

Polynomials
CBSE Most Repeated PYQs

Solve official CBSE Previous Year Board Questions (2015-2024) for Polynomials. Click on options to test yourself, or click "Show Solution & Answer" for complete step-by-step working.

Q1CBSE 2024, 2020MCQ

1 Mark

If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is:

Q2CBSE 2023, 2019MCQ

1 Mark

A quadratic polynomial whose zeroes are -3 and 4 is:

Q3CBSE 2022, 2018MCQ

1 Mark

If α and β are zeroes of px² - 2x + 3p and α + β = αβ, then p is:

Q4CBSE 2024, 2021MCQ

1 Mark

If α, β are zeroes of x² - 4x + 1, then value of 1/α + 1/β - αβ is:

Q5CBSE 2023, 2017Assertion-Reason

1 Mark

Assertion (A): Degree of zero polynomial is not defined. Reason (R): Degree of a non-zero constant polynomial is 0.

Q6CBSE 2020, 2016Assertion-Reason

1 Mark

Assertion (A): Polynomial p(x) = x² + 4x + 5 has no real zeroes. Reason (R): A quadratic polynomial with discriminant D < 0 has no real zeroes.

Q7CBSE 2024, 2020Short Answer

2 Marks

Find zeroes of quadratic polynomial x² + 7x + 10.

Q8CBSE 2023, 2019Short Answer

2 Marks

Verify relationship between zeroes and coefficients for x² - 2x - 8.

Q9CBSE 2022, 2018Short Answer

2 Marks

Find quadratic polynomial whose sum and product of zeroes are -3 and 2.

Q10CBSE 2024, 2021Short Answer

2 Marks

Find zeroes of 4s² - 4s + 1.

Q11CBSE 2023, 2017Short Answer

2 Marks

Find zeroes of t² - 15.

Q12CBSE 2020, 2016Long Answer

3 Marks

If α, β are zeroes of x² - p(x + 1) - c, show (α + 1)(β + 1) = 1 - c.

Q13CBSE 2024, 2020Long Answer

3 Marks

Find zeroes of 6x² - 3 - 7x and verify relationships.

Q14CBSE 2023, 2019Long Answer

3 Marks

If α, β are zeroes of x² - 6x + k and 3α + 2β = 20, find k.

Q15CBSE 2022, 2018Long Answer

3 Marks

Find polynomial whose zeroes are reciprocal to zeroes of ax² + bx + c.

Q16CBSE 2024, 2021Case Study

4 Marks

Case Study Scenario: A highway underpass is parabolic in shape represented by quadratic polynomial p(x) = -x² + 2x + 8. Question: Find zeroes of the polynomial and maximum height of underpass.

Q17CBSE 2023, 2017Case Study

4 Marks

Case Study Scenario: An engine displacement is modeled by polynomial p(t) = 3t² - 5t - 2. Question: Find zeroes of polynomial representing engine equilibrium times.

Q18CBSE Official Board PYQPYQ

5 Marks

If α, β are zeroes of f(x) = x² - 4x + 3, find α⁴β³ + α³β⁴.

Q19CBSE Official Board PYQPYQ

5 Marks

If sum of zeroes of ky² + 2y + 3k equals their product, find k.

Q20CBSE Official Board PYQPYQ

5 Marks

Polynomials CBSE Most Repeated PYQs

If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is:

A quadratic polynomial whose zeroes are -3 and 4 is:

If α and β are zeroes of px² - 2x + 3p and α + β = αβ, then p is:

If α, β are zeroes of x² - 4x + 1, then value of 1/α + 1/β - αβ is:

Assertion (A): Degree of zero polynomial is not defined. Reason (R): Degree of a non-zero constant polynomial is 0.

Assertion (A): Polynomial p(x) = x² + 4x + 5 has no real zeroes. Reason (R): A quadratic polynomial with discriminant D < 0 has no real zeroes.

Find zeroes of quadratic polynomial x² + 7x + 10.

Verify relationship between zeroes and coefficients for x² - 2x - 8.

Find quadratic polynomial whose sum and product of zeroes are -3 and 2.

Find zeroes of 4s² - 4s + 1.

Find zeroes of t² - 15.

If α, β are zeroes of x² - p(x + 1) - c, show (α + 1)(β + 1) = 1 - c.

Find zeroes of 6x² - 3 - 7x and verify relationships.

If α, β are zeroes of x² - 6x + k and 3α + 2β = 20, find k.

Find polynomial whose zeroes are reciprocal to zeroes of ax² + bx + c.

Case Study Scenario: A highway underpass is parabolic in shape represented by quadratic polynomial p(x) = -x² + 2x + 8. Question: Find zeroes of the polynomial and maximum height of underpass.

Case Study Scenario: An engine displacement is modeled by polynomial p(t) = 3t² - 5t - 2. Question: Find zeroes of polynomial representing engine equilibrium times.

If α, β are zeroes of f(x) = x² - 4x + 3, find α⁴β³ + α³β⁴.

If sum of zeroes of ky² + 2y + 3k equals their product, find k.

Find quadratic polynomial whose zeroes are (2 + √3) and (2 - √3).

Polynomials
CBSE Most Repeated PYQs