Polynomials: Class 10 Previous Year Questions

Polynomials questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. Find the zeroes of the polynomial p(x) = 3x2 2x 1 and verify the relationship between the zeroes of p(x) and the coefficients of p(x).
   Board 20253 marksshort answerRepeated: 2023,2024,2025
2. (a) Zeroes of the quadratic polynomial x2 – 3x + 2 are a and b. Construct a quadratic polynomial whose zeroes are 2a + 1 and 2b + 1. 3 OR (b) Find the zeroes of the polynomial 4x2 – 4x + 1 and verify the relationship between the zeroes and the coefficients.
   Board 20243 marksshort answerRepeated: 2023,2024,2025
3. Find the zeroes of the polynomial p(x) = 2x2 7x 15 and verify the relationship between its coefficients and zeroes.
   Board 20233 marksshort answerRepeated: 2023,2024,2025
4. Find a quadratic polynomial whose sum and product of zeroes are 0 and 9, respectively. Also, find the zeroes of the polynomial so obtained.
   Board 20253 marksshort answerRepeated: 2024,2025
5. A quadratic polynomial, the sum of whose zeroes is –5 and their product is 6, is 1 (A) x2 + 5x + 6 (B) x2 – 5x + 6 (C) x2 – 5x – 6 (D) –x2 + 5x +
   Board 20241 markMCQRepeated: 2024,2025
6. For what value of k, the product of zeroes of the polynomial kx? -4x-7 is 2 ? 1 (a) (b) (c) (d) 14
   Board 20241 markMCQ
7. The height and radius of a right circular cone are 24 cm and 7 cm respectively. The slant height of the cone is : (c) 26 cm (a)24 cm (b) 31 cm (d) 25 cm 15.1 If one of the zeroes of the quadratic polynomial (· -1)x? +·x+1 is -3, then the value of · is : (b) (a…
   Board 20241 markMCQ
8. Assertion (A) : Zeroes of a polynomial p(x) = x- -2x-3 are -1 and 3. Reason (R) : The graph of polynomial p(x)= x2 -2x-3 intersects x-axis at (-1, 0) and (3, 0).
   Board 20241 markAssertion-Reason
9. If ·, · are zeroes of the quadratic polynomial x2 + 3x + 2, find a quadratic polynomial whose zeroes are · + 1, · + 1.
   Board 20233 marksshort answer
10. The sum and the product of zeroes of the polynomial p(x) = x2 + 5x + 6 are respectively (a) 5, -6 (b) - 5, 6 (c) 2, 3 (d) -2, -3 Page 7 11. 5- (b) (a) (c) (d) 12100100 100m 100V3 m 06 (b) (a) 60° 45° (d) (c) 30° 13. (b) (a) 3 r8 3 ·r3 (c) 9 ·r3 (d) rr3 14. (b)…
    Board 20231 markMCQ
11. The graph of y = p(·) is shown in the figure for some polynomial p(x). The number of zeroes of p(·) is/are : p(x) >x (a) (b) (c) (d)
    Board 20231 markMCQ
12. Graph of a polynomial p(x) is given in the figure. The number of zeroes of p(x) is : (a) 2 (b) 3 (c) 4 (d)
    Board 20231 markMCQ
13. Assertion (A) : Polynomial x2 + 4x has two real zeroes. Reason (R) : Zeroes of the polynomial x2 + ax ( ) are 0 and a.
    Board 20231 markAssertion-Reason

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