01 · CBSE BOARD EXAM 2024
CBSE 2024 Board Practice Questions
CBSE 2024 · 1 MARK
Q1. If one zero of the quadratic polynomial x² + 3x + k is 2, then find the value of k.
CBSE 2024 · 1 MARK
Q2. The number of polynomials having zeroes -2 and 5 is:
(A) 1 (B) 2 (C) 3 (D) More than 3
CBSE 2024 · 2 MARKS
Q3. Find the zeroes of the quadratic polynomial 6x² - 3 - 7x and verify the relationship between the zeroes and coefficients.
CBSE 2024 · 3 MARKS
Q4. If α and β are the zeroes of the quadratic polynomial p(x) = x² - p(x + 1) - c, prove that (α + 1)(β + 1) = 1 - c.
CBSE 2024 · 3 MARKS
Q5. If α and β are zeroes of x² - 6x + a, find the value of a if 3α + 2β = 20.
02 · CBSE BOARD EXAM 2023
CBSE 2023 Board Practice Questions
CBSE 2023 · 1 MARK
Q6. If α and β are zeroes of p(x) = 2x² + 5x + k such that α² + β² + αβ = 21/4, find the value of k.
CBSE 2023 · 1 MARK
Q7. A quadratic polynomial, the sum of whose zeroes is -3 and product is 2, is:
(A) x² + 3x + 2 (B) x² - 3x + 2 (C) x² + 3x - 2 (D) -x² + 3x + 2
CBSE 2023 · 2 MARKS
Q8. Find a quadratic polynomial whose zeroes are reciprocal of the zeroes of the polynomial f(x) = ax² + bx + c (a ≠ 0, c ≠ 0).
CBSE 2023 · 3 MARKS
Q9. If α and β are zeroes of the polynomial k x² + 4x + 4 such that α² + β² = 24, find the value of k.
03 · CBSE BOARD EXAM 2022
CBSE 2022 Board Practice Questions
CBSE 2022 · 1 MARK
Q10. If one zero of 3x² + 8x + k is the reciprocal of the other, find the value of k.
CBSE 2022 · 2 MARKS
Q11. Find the zeroes of 4x² - 4x + 1 and verify the relationship between zeroes and coefficients.
CBSE 2022 · 3 MARKS
Q12. Find a quadratic polynomial whose zeroes are 2 + √3 and 2 - √3.
04 · CBSE BOARD EXAM 2021
CBSE 2021 Board Practice Questions
CBSE 2021 · 1 MARK
Q13. If the product of zeroes of the polynomial ax² - 6x - 6 is 4, find the value of a.
CBSE 2021 · 3 MARKS
Q14. If α and β are zeroes of x² - 4x + 3, form a quadratic polynomial whose zeroes are 3α and 3β.
05 · CBSE BOARD EXAM 2020
CBSE 2020 Board Practice Questions
CBSE 2020 · 1 MARK
Q15. If α and β are the zeroes of p(x) = x² - 5x + 6, find the value of α + β - 3αβ.
CBSE 2020 · 2 MARKS
Q16. Find the zeroes of x² - 2x - 8 and verify the relationship between the zeroes and coefficients.
CBSE 2020 · 3 MARKS
Q17. If α and β are the zeroes of the quadratic polynomial f(x) = x² - 1, find a quadratic polynomial whose zeroes are 2α/β and 2β/α.
06 · SELF-PRACTICE TIPS
Tips for Solving Board PYQs
01
Always write down α + β = -b/a and αβ = c/a first before simplifying algebra.
02
Use identities like α² + β² = (α + β)² - 2αβ to evaluate expressions without finding roots.
03
When zeroes are reciprocal (α and 1/α), product of zeroes α · (1/α) = 1 ⟹ c/a = 1 ⟹ c = a!