Chapter Exam

Chapter-2-POLYNOMIALS — Online MCQ Test

Q: What is the degree of the polynomial 3x⁴ + 2x³ - x + 5?

Answer: D. 4 — The degree of a polynomial is the highest exponent of the variable, which is 4 in this polynomial.

Q: For what value of k is (-4) a zero of the polynomial x² - x - (2k + 2)?

Answer: B. k = 9 — Substituting x = -4: (-4)² - (-4) - (2k+2) = 0 → 16 + 4 - 2k - 2 = 0 → 18 = 2k → k = 9.

Q: If one zero of the quadratic polynomial (k-1)x² + kx + 1 is -3, find k:

Answer: A. k = 4/3 — Substituting x = -3: (k-1)(9) + k(-3) + 1 = 0 → 9k - 9 - 3k + 1 = 0 → 6k = 8 → k = 4/3.

Q: If α and β are the zeroes of 2x² + 5x + k satisfying α² + β² + αβ = 21/4, find k:

Answer: A. k = 2 — α+β = -5/2, αβ = k/2. α²+β²+αβ = (α+β)²-αβ = 25/4 - k/2 = 21/4. So k/2 = 25/4 - 21/4 = 1, giving k = 2.

MATHS · Grade 10 · CBSE(NCERT)

Practice Chapter-2-POLYNOMIALS with a free chapter-wise online MCQ test for CBSE(NCERT) Grade 10 MATHS. This chapter covers: POLYNOMIALS. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter-2-POLYNOMIALS — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 10 MATHS — Chapter-2-POLYNOMIALS, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is a polynomial?

A. An expression with variables having negative integer exponents
B. A mathematical expression with variables and coefficients where exponents are non-negative integers ✓
C. An expression involving only addition and subtraction of numbers
D. An algebraic expression with fractional powers of variables

Answer: B. A mathematical expression with variables and coefficients where exponents are non-negative integers
A polynomial consists of variables and coefficients where the exponent of each variable is a non-negative integer, distinguishing it from other algebraic expressions.

What is the degree of the polynomial 3x⁴ + 2x³ - x + 5?

A. 1
B. 2
C. 3
D. 4 ✓

Answer: D. 4
The degree of a polynomial is the highest exponent of the variable, which is 4 in this polynomial.

For what value of k is (-4) a zero of the polynomial x² - x - (2k + 2)?

A. k = 7
B. k = 9 ✓
C. k = 8
D. k = 5

Answer: B. k = 9
Substituting x = -4: (-4)² - (-4) - (2k+2) = 0 → 16 + 4 - 2k - 2 = 0 → 18 = 2k → k = 9.

If one zero of the quadratic polynomial (k-1)x² + kx + 1 is -3, find k:

A. k = 4/3 ✓
B. k = -4/3
C. k = 2/3
D. k = -2/3

Answer: A. k = 4/3
Substituting x = -3: (k-1)(9) + k(-3) + 1 = 0 → 9k - 9 - 3k + 1 = 0 → 6k = 8 → k = 4/3.

If α and β are the zeroes of 2x² + 5x + k satisfying α² + β² + αβ = 21/4, find k:

A. k = 2 ✓
B. k = 3
C. k = 4
D. k = 1

Answer: A. k = 2
α+β = -5/2, αβ = k/2. α²+β²+αβ = (α+β)²-αβ = 25/4 - k/2 = 21/4. So k/2 = 25/4 - 21/4 = 1, giving k = 2.

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