Post-Chapter Assessment - Chapter 3: Polynomials
Pattern: 20 questions × 1 mark = 20 marks. Choose the correct option for each question.
1. Which of the following is a polynomial in \(x\)?
- A) \(\frac{1}{x} + 2\)
- B) \(2x^3 - 5x + 7\)
- C) \(x^{-2} + 3\)
- D) \(\sqrt{x} + 1\)
Answer: B
2. The degree of \(5x^3 - 2x^2 + 7x - 4\) is:
Answer: B
3. A polynomial of degree 2 is called:
- A) Linear polynomial
- B) Cubic polynomial
- C) Quadratic polynomial
- D) Constant polynomial
Answer: C
4. The value of \(p(x) = x^2 - 2x - 3\) at \(x = 1\) is:
Answer: C
5. A real number \(k\) is a zero of \(p(x)\) if:
- A) \(p(k) = 1\)
- B) \(p(k) = 0\)
- C) \(p(k) = k\)
- D) \(p(0) = k\)
Answer: B
6. The zero of \(2x + 5\) is:
- A) \(\frac{5}{2}\)
- B) \(-\frac{5}{2}\)
- C) \(\frac{2}{5}\)
- D) \(-\frac{2}{5}\)
Answer: B
7. The graph of a linear polynomial \(y = ax + b\), \(a \neq 0\), is:
- A) Circle
- B) Parabola
- C) Straight line
- D) Ellipse
Answer: C
8. The zeroes of a polynomial are the x-coordinates of the points where its graph:
- A) Intersects the Y-axis
- B) Intersects the X-axis
- C) Meets the origin only
- D) Is parallel to the X-axis
Answer: B
9. The polynomial \(x^2 - 3x - 4\) has zeroes:
- A) 1, 4
- B) -1, 4
- C) -1, -4
- D) 1, -4
Answer: B
10. A quadratic polynomial can have at most:
- A) 1 zero
- B) 2 zeroes
- C) 3 zeroes
- D) 4 zeroes
Answer: B
11. If the zeroes of \(ax^2 + bx + c\) are \(\alpha, \beta\), then \(\alpha + \beta\) is:
- A) \(\frac{b}{a}\)
- B) \(-\frac{b}{a}\)
- C) \(\frac{c}{a}\)
- D) \(-\frac{c}{a}\)
Answer: B
12. If the zeroes of \(ax^2 + bx + c\) are \(\alpha, \beta\), then \(\alpha\beta\) is:
- A) \(\frac{b}{a}\)
- B) \(-\frac{b}{a}\)
- C) \(\frac{c}{a}\)
- D) \(-\frac{c}{a}\)
Answer: C
13. The sum of the zeroes of \(x^2 + 7x + 10\) is:
Answer: B
14. The product of the zeroes of \(2x^2 - 8x + 6\) is:
Answer: B
15. A cubic polynomial can have at most:
- A) 1 zero
- B) 2 zeroes
- C) 3 zeroes
- D) 4 zeroes
Answer: C
16. If \(\alpha, \beta, \gamma\) are zeroes of \(ax^3 + bx^2 + cx + d\), then:
- A) \(\alpha + \beta + \gamma = \frac{b}{a}\)
- B) \(\alpha + \beta + \gamma = -\frac{b}{a}\)
- C) \(\alpha + \beta + \gamma = \frac{c}{a}\)
- D) \(\alpha + \beta + \gamma = -\frac{d}{a}\)
Answer: B
17. If \(p(x)\) is divided by \(x - a\), the remainder is:
- A) \(p(0)\)
- B) \(p(1)\)
- C) \(p(a)\)
- D) \(p(-a)\)
Answer: C
18. In the division algorithm for polynomials:
- A) Dividend = Divisor + Quotient + Remainder
- B) Dividend = Divisor × Quotient + Remainder
- C) Dividend = Divisor × Remainder + Quotient
- D) Dividend = Quotient - Divisor + Remainder
Answer: B
19. When a polynomial is divided by a polynomial of degree 2, the degree of the remainder must be:
- A) Greater than 2
- B) Equal to 2
- C) Less than 2
- D) Always 0
Answer: C
20. If the remainder is zero when \(p(x)\) is divided by \(g(x)\), then:
- A) \(g(x)\) is a factor of \(p(x)\)
- B) \(p(x)\) is a constant
- C) \(g(x)\) is not related to \(p(x)\)
- D) \(p(x)\) has no zeroes
Answer: A
Answer Key
| Q. No. |
Ans. |
Q. No. |
Ans. |
| 1 | B | 11 | B |
| 2 | B | 12 | C |
| 3 | C | 13 | B |
| 4 | C | 14 | B |
| 5 | B | 15 | C |
| 6 | B | 16 | B |
| 7 | C | 17 | C |
| 8 | B | 18 | B |
| 9 | B | 19 | C |
| 10 | B | 20 | A |
