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Class 10 Maths Chapter 2 Polynomials MCQs
Board | CBSE Board, UP Board, JAC Board, Bihar Board, HBSE Board, UBSE Board, PSEB Board, RBSE Board, JK Board |
Textbook | NCERT |
Class | Class 10 |
Subject | Maths |
Chapter | Polynomials |
Post Type | Study Material |
Medium | Hindi/English |
1. If one zero of the polynomial p(x) = 2x2 – 7x + 3 is 3, what is the other zero?
A) 1/2
B) 3/2
C) -1
D) -3
Answer: B) 3/2
Explanation: Using the relation (Sum of zeros = 7/2), we get the other zero as 3/2.
2. The degree of the polynomial 5x4 – 3x3 + 2 is:
A) 4
B) 3
C) 2
D) 1
Answer: A) 4
Explanation: The highest power of x is 4, so the degree is 4.
3. The zero of the polynomial p(x) = x – 5 is:
A) 5
B) -5
C) 1
D) 0
Answer: A) 5
Explanation: Setting x – 5 = 0, we get x = 5 as the zero.
4. The polynomial x2 – 5x + 6 has:
A) One real root
B) No real roots
C) Two distinct real roots
D) Infinite roots
Answer: C) Two distinct real roots
Explanation: Factorizing gives (x – 2)(x – 3) = 0, so x = 2 and x = 3 are the roots.
5. The value of k if x = 2 is a root of the polynomial p(x) = x2 – kx + 3 is:
A) 3
B) 4
C) 6
D) 5
Answer: C) 6
Explanation: Substitute x = 2, so 4 – 2k + 3 = 0; solving gives k = 6.
6. If ╬▒ and ╬▓ are the zeros of the polynomial p(x) = x2 – 5x + 6, then ╬▒ + ╬▓ equals:
A) -5
B) 5
C) 6
D) 1
Answer: B) 5
Explanation: Sum of zeros ╬▒ + ╬▓ = -coefficient of x / coefficient of x2 = 5.
7. Which of the following is a quadratic polynomial?
A) 3x + 4
B) x2 – 4x + 3
C) x3 + 2
D) 2x
Answer: B) x2 – 4x + 3
Explanation: A quadratic polynomial has a degree of 2.
8. The product of the zeros of the polynomial p(x) = 2x2 – 3x + 1 is:
A) 1/2
B) 2
C) -3
D) 1
Answer: A) 1/2
Explanation: Product of zeros = constant term / coefficient of x2 = 1/2.
9. A polynomial of degree 0 is called:
A) Linear
B) Quadratic
C) Constant
D) Cubic
Answer: C) Constant
Explanation: Polynomials of degree 0 are constant as they do not contain x.
10. If the zero of the polynomial x2 + kx + 6 is -2, then k is:
A) -4
B) 4
C) -6
D) 6
Answer: B) 4
Explanation: Substitute x = -2, so 4 – 2k + 6 = 0; solving gives k = 4.
11. If ╬▒ and ╬▓ are the zeros of the polynomial p(x) = x2 + 6x + 8, then ╬▒╬▓ equals:
A) 6
B) 8
C) -8
D) -6
Answer: B) 8
Explanation: Product of zeros ╬▒╬▓ = constant term / coefficient of x2 = 8.
12. For the polynomial p(x) = x2 – 4x + 4, the sum and product of its zeros are:
A) 4 and 4
B) -4 and 4
C) 2 and 4
D) 4 and 2
Answer: A) 4 and 4
Explanation: Sum of zeros = 4, Product of zeros = 4 for x2 – 4x + 4.
13. The polynomial x3 – 3x2 + 3x – 1 has:
A) One zero
B) Two zeros
C) Three zeros
D) No zeros
Answer: C) Three zeros
Explanation: A cubic polynomial (degree 3) has exactly three zeros.
14. Which of the following polynomial expressions represents a linear polynomial?
A) x3 – 2
B) 5x + 1
C) x2 – x
D) x – x2 + 3
Answer: B) 5x + 1
Explanation: A linear polynomial has degree 1, which is seen in 5x + 1.
15. The sum of the zeros of the polynomial x2 – 9x + 20 is:
A) 9
B) -9
C) 20
D) -20
Answer: A) 9
Explanation: Sum of zeros = -coefficient of x / coefficient of x2 = 9.
16. The polynomial 4x2 – 12x + 9 has a zero equal to:
A) 3
B) -3
C) 3/2
D) -3/2
Answer: C) 3/2
Explanation: Factoring gives (2x – 3)2, so x = 3/2 is the zero.
17. The zeros of the polynomial x2 – 1 are:
A) ┬▒1
B) 1 and 0
C) 0 and -1
D) ┬▒2
Answer: A) ┬▒1
Explanation: Factoring x2 – 1 gives (x + 1)(x – 1) = 0, so x = ┬▒1.
18. Which of these has a degree of 1?
A) 3x2 – 5x
B) 7x – 8
C) x3 + 2x
D) 4x2 – x + 1
Answer: B) 7x – 8
Explanation: Degree of 7x – 8 is 1, making it a linear polynomial.
19. If ╬▒ and ╬▓ are the zeros of x2 – 4, then ╬▒╬▓ is:
A) -4
B) 4
C) 0
D) 2
Answer: B) 4
Explanation: Product of zeros ╬▒╬▓ = constant term (4) / coefficient of x2 = 4.
20. The value of k for which x = -3 is a zero of the polynomial x2 + kx + 12 is:
A) 6
B) -6
C) 4
D) -4
Answer: A) 6
Explanation: Substitute x = -3, giving 9 – 3k + 12 = 0; solving gives k = 6.
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