MCQs on Chapter 2 'Polynomials' for Class 10 Maths

MCQs on Chapter 2: Polynomials for Class 10 are available in this Maths article along with a free PDF for offline practice. These multiple‑choice questions help students practise the key concepts from Chapter 2 of the CBSE Maths syllabus in an exam‑oriented format. The MCQs with answers and detailed solutions, prepared by our subject experts, cover zeroes of polynomials, the relationship between zeroes and coefficients, division algorithm for polynomials, and the geometric meaning of zeroes to strengthen conceptual understanding and improve problem‑solving skills. By practising MCQs on Chapter 2: Polynomials, students can improve accuracy, understand formulas better, and build confidence for board exams.

 

MCQS on Chapter 2: Polynomials for Class 10 With Answers

Question 1: The degree of the polynomial 7u⁶ – (3/2)u⁴ + 4u² + u – 8 is:

(A) 2

(B) 4

(C) 6

(D) 8

Answer: (C) 6

Explanation: The highest power of u is 6, so the degree is 6.

Question 2: Which of the following expressions is NOT a polynomial?

(A) 4x + 2

(B) 2y² – 3y + 4

(C) 1/(x – 1)

(D) 3z³ – z + 5

Answer: (C) 1/(x – 1)

Explanation: 1/(x–1) = (x–1)^(–1) has a negative integer exponent. Polynomials can only have non-negative integer powers of the variable.

Question 3: The most general form of a cubic polynomial is:

(A) ax² + bx + c, a ≠ 0

(B) ax³ + bx² + cx + d, a ≠ 0

(C) ax + b, a ≠ 0

(D) ax⁴ + bx³ + cx² + dx + e, a ≠ 0

Answer: (B) ax³ + bx² + cx + d, a ≠ 0

Explanation: A cubic polynomial has degree 3. Its most general form includes terms up to x³, with the leading coefficient a ≠ 0.

Question 4: The zero of the linear polynomial ax + b (a ≠ 0) is:

(A) a/b

(B) –a/b

(C) b/a

(D) –b/a

Answer: (D) –b/a

Explanation: If k is a zero, then ak + b = 0, which gives k = –b/a.

Question 5: How many zeroes can a polynomial of degree n have, at most?

(A) n – 1

(B) n

(C) n + 1

(D) 2n

Answer: (B) n

Explanation: The graph of y = p(x), where p(x) has degree n, can intersect the x-axis at most n times. Therefore, a polynomial of degree n has at most n zeroes.

Question 6: The zeroes of the polynomial p(x) = x² – 3x – 4 are:

(A) 1 and –4

(B) –1 and 4

(C) 3 and –4

(D) –1 and –4

Answer: (B) –1 and 4

Explanation: p(–1) = 1 + 3 – 4 = 0 and p(4) = 16 – 12 – 4 = 0. So –1 and 4 are both zeroes.

Question 7: The graph of a linear polynomial y = ax + b (a ≠ 0) intersects the x-axis at:

(A) No point

(B) Exactly one point

(C) Exactly two points

(D) More than two points

Answer: (B) Exactly one point

Explanation: A straight line that is not parallel to the x-axis will always cut the x-axis at exactly one point: at (–b/a, 0). This is consistent with a linear polynomial having exactly one zero.

Question 8: For the cubic polynomial y = x³ – 4x, the table of values gives y = 0 when x = –2, 0, and 2. What does this tell us about the graph?

(A) The graph is tangent to the x-axis

(B) The graph intersects the x-axis at exactly three points

(C) The graph never crosses the x-axis

(D) The graph intersects the x-axis at two points

Answer: (B) The graph intersects the x-axis at exactly three points

Explanation: From the table for y = x³ – 4x, y = 0 at x = –2, 0, and 2. These are the three zeroes, and geometrically the graph crosses the x-axis at three distinct points.

Question 9: If the parabola representing y = ax² + bx + c touches the x-axis at exactly one point, the quadratic polynomial has:

(A) Two distinct zeroes

(B) No real zeroes

(C) Exactly one zero (two equal zeroes)

(D) Three zeroes

Answer: (C) Exactly one zero (two equal zeroes)

Explanation: When the parabola is tangent to the x-axis, the two zeroes coincide, that is, α = β.

Question 10: If α and β are the zeroes of the polynomial ax² + bx + c, then αβ equals:

(A) –b/a

(B) b/c

(C) c/a

(D) –c/a

Answer: (C) c/a

Explanation: The product of the zeroes of ax² + bx + c is c/a = (constant term) / (coefficient of x²).

Question 11: For the polynomial p(x) = 2x³ – 5x² – 14x + 8 with zeroes 4, –2, and 1/2, the sum of the products of zeroes taken two at a time equals:

(A) 14/2

(B) –7

(C) –14/2

(D) 5/2

Answer: (C) –14/2 = –7

Explanation: αβ + βγ + γα = c/a = –14/2 = –7. 

{4×(–2)} + {(–2)×(1/2)} + {(1/2)×4} = –8 – 1 + 2 = –7

Question 12: For a cubic polynomial ax³ + bx² + cx + d with zeroes α, β, γ, which relationship is CORRECT?

(A) αβ + βγ + γα = –c/a

(B) αβ + βγ + γα = c/a

(C) αβ + βγ + γα = d/a

(D) αβ + βγ + γα = –b/a

Answer: (B) αβ + βγ + γα = c/a

Explanation: The three Vieta's formulas for a cubic are: sum of zeroes = –b/a; sum of products of zeroes taken two at a time = c/a; product of all three zeroes = –d/a. 

Question 13: If the sum and product of the zeroes of kx² + 2x + 3k are equal, then k equals:

(A) 1/3

(B) –1/3

(C) 3

(D) –3

Answer: (B) –1/3

Explanation: Sum = –2/k; product = 3k/k = 3. Setting them equal: –2/k = 3 ⇒ k = –2/3.

Question 14: The zeroes of the polynomial x² – 3 are:

(A) ±3

(B) ±√3

(C) 0 and 3

(D) ±1/√3

Answer: (B) ±√3

Explanation: x² – 3 = (x – √3)(x + √3), giving zeroes √3 and –√3.

Question 15: A quadratic polynomial with zeroes 2 and –3 is:

(A) x² + x – 6

(B) x² – x – 6

(C) x² + x + 6

(D) x² – x + 6

Answer: (A) x² + x – 6

Explanation: Sum of zeroes = 2 + (–3) = –1; product = 2 × (–3) = –6. Polynomial = x² – (sum)x + product = x² – (–1)x + (–6) = x² + x – 6. 

 

Click here to download the free PDF of MCQs worksheet on Chapter 2: Polynomials for Class 10 Maths based on the updated NCERT & CBSE pattern with important multiple-choice questions and answers.

MCQs Worksheet on Chapter 2: Polynomials for Class 10