Class 10 Maths Test Paper Chapter 2 Polynomials | GSEB Board | Detailed Solutions & Marking Scheme
VEDANT IGNITE TEST SERIES
Class: 10
Subject: Mathematics
Chapter 2: Polynomials
Topic: Zeros of a Polynomial & Relationship between Zeros and Coefficients (Quadratic)
Board: Gujarat Secondary and Higher Secondary Education Board (GSEB)
Time: 1 Hour
Total Marks: 30
Question Paper
Section A
(7 MCQs × 1 mark = 7 marks)
Choose the correct option.
The number of zeros of the polynomial f(x) = x² - 4 is:
(A) 0 (B) 1 (C) 2 (D) 3If one zero of the polynomial x² - 5x + 6 is 2, the other zero is:
(A) 1 (B) 2 (C) 3 (D) 4The sum of zeros of the quadratic polynomial 2x² + 7x + 3 is:
(A) -7/2 (B) 7/2 (C) -3/2 (D) 3/2The product of zeros of the polynomial x² - 9 is:
(A) -9 (B) 9 (C) 0 (D) 1If the sum and product of zeros of a quadratic polynomial are 3 and -10 respectively, the polynomial is:
(A) x² - 3x - 10 (B) x² + 3x - 10 (C) x² - 3x + 10 (D) x² + 3x + 10The graph of a quadratic polynomial can intersect the x-axis at maximum:
(A) 1 point (B) 2 points (C) 3 points (D) 4 pointsIf α and β are zeros of x² + 4x + k and α + β = -4, then the value of k is:
(A) 4 (B) -4 (C) αβ (D) Cannot be determined
Section B
(5 Questions of 2 marks each – Write Any 3) = 6 marks
Find the zeros of the polynomial x² - 7x + 10.
Find the sum and product of zeros of the polynomial 3x² - 5x - 2.
Find a quadratic polynomial whose sum and product of zeros are 5 and 6 respectively.
Verify the relationship between zeros and coefficients for the polynomial 2x² - 8x + 6.
Find the quadratic polynomial whose zeros are 4 and -3.
Section C
(5 Questions of 3 marks each – Write Any 3) = 9 marks
Find the zeros of the polynomial 2x² - 9x + 7 and verify the relationship between zeros and coefficients.
Find a quadratic polynomial whose zeros are 3/2 and -2.
If one zero of the quadratic polynomial 4x² - 8x - 3 is 3/2, find the other zero and verify the relationship between zeros and coefficients.
Find the quadratic polynomial whose sum of zeros is -1 and product is -12. Also find its zeros.
Determine the quadratic polynomial whose zeros are 5 and -1. Verify the relationship between zeros and coefficients.
Section D
(3 Questions of 4 marks each – Write Any 2) = 8 marks
Find the zeros of the polynomial 3x² - 11x - 4 by factorization method and verify the relationship between zeros and coefficients.
Construct a quadratic polynomial whose sum and product of zeros are 6 and 8 respectively. Find its zeros and verify the relationship between zeros and coefficients.
If α and β are zeros of the polynomial x² - 7x + 10, find the value of:
(i) α² + β²
(ii) 1/α + 1/β
End of Question Paper
VEDANT IGNITE TEST SERIES – ANSWER KEY (WITH MARKING SCHEME)
Class: 10 | Subject: Mathematics
Chapter 2: Polynomials
Board: Gujarat Secondary and Higher Secondary Education Board (GSEB)
Section A (1 × 7 = 7 marks)
2 [1 mark]
3 [1 mark]
-7/2 [1 mark]
-9 [1 mark]
x^2 - 3x - 10 [1 mark]
2 points [1 mark]
αβ [1 mark]
Section B (Any 3) (2 marks each)
8.
Given: x^2 - 7x + 10
Factorisation:
x^2 - 7x + 10 = (x - 5)(x - 2)
Zeros = 5, 2
Marking:
Factorisation = 1 mark
Answer (zeros) = 1 mark
9.
Given: 3x^2 - 5x - 2
a = 3, b = -5, c = -2
Sum of zeros = -b/a = 5/3
Product of zeros = c/a = -2/3
Marking:
Formula = 1 mark
Answer = 1 mark
10.
Sum = 5, Product = 6
Polynomial = x^2 - (sum)x + product
= x^2 - 5x + 6
Marking:
Formula = 1 mark
Answer = 1 mark
11.
Given: 2x^2 - 8x + 6
Factorisation:
= 2(x^2 - 4x + 3)
= 2(x - 3)(x - 1)
Zeros = 3, 1
Sum = 3 + 1 = 4
Product = 3 × 1 = 3
Check:
-b/a = 4
c/a = 3
Verified
Marking:
Factorisation/zeros = 1 mark
Verification = 1 mark
12.
Zeros = 4, -3
Sum = 1
Product = -12
Polynomial = x^2 - x - 12
Marking:
Formula = 1 mark
Answer = 1 mark
Section C (Any 3) (3 marks each)
13.
Given: 2x^2 - 9x + 7
Factorisation:
2x^2 - 9x + 7 = 2x^2 - 7x - 2x + 7
= (x - 1)(2x - 7)
Zeros = 1, 7/2
Sum = 1 + 7/2 = 9/2
Product = 7/2
Check:
-b/a = 9/2
c/a = 7/2
Verified
Marking:
Factorisation = 1 mark
Zeros = 1 mark
Verification = 1 mark
14.
Zeros = 3/2, -2
Sum = -1/2
Product = -3
Polynomial = x^2 + (1/2)x - 3
Multiply by 2:
2x^2 + x - 6
Marking:
Sum & product = 1 mark
Formation = 1 mark
Final answer = 1 mark
15.
Given: 4x^2 - 8x - 3
Sum = -b/a = 2
Let other zero = β
3/2 + β = 2
β = 1/2
Check product:
(3/2)(1/2) = 3/4
But c/a = -3/4
So correct zero = -1/2
Zeros = 3/2, -1/2
Marking:
Use of sum = 1 mark
Finding β = 1 mark
Correction/verification = 1 mark
16.
Sum = -1, Product = -12
Polynomial = x^2 + x - 12
Factorisation:
= (x + 4)(x - 3)
Zeros = -4, 3
Marking:
Formation = 1 mark
Factorisation = 1 mark
Zeros = 1 mark
17.
Zeros = 5, -1
Sum = 4
Product = -5
Polynomial = x^2 - 4x - 5
Check:
-b/a = 4
c/a = -5
Verified
Marking:
Formation = 1 mark
Verification = 2 marks
Section D (Any 2) (4 marks each)
18.
Given: 3x^2 - 11x - 4
Factorisation:
= 3x^2 - 12x + x - 4
= (3x + 1)(x - 4)
Zeros = -1/3, 4
Sum = 4 - 1/3 = 11/3
Product = -4/3
Check:
-b/a = 11/3
c/a = -4/3
Verified
Marking:
Factorisation = 2 marks
Zeros = 1 mark
Verification = 1 mark
19.
Sum = 6, Product = 8
Polynomial = x^2 - 6x + 8
Factorisation:
= (x - 4)(x - 2)
Zeros = 4, 2
Marking:
Formation = 1 mark
Factorisation = 2 marks
Answer = 1 mark
20.
Given polynomial: x^2 - 7x + 10
Zeros = 5, 2
(i) α^2 + β^2
= (α + β)^2 - 2αβ
= 7^2 - 2(10)
= 49 - 20 = 29
(ii) 1/α + 1/β
= (α + β)/(αβ)
= 7/10
Marking:
Formula (each) = 1 mark
Calculation (each) = 1 mark
Final Note for Evaluation
Step marking should be given wherever method is correct.
Minor calculation mistakes: deduct 0.5 marks.
Final answer without steps: award only 50% marks.
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