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Chapter-2-POLYNOMIALS — Online MCQ Test

MATHS · CLASS 10th · Karnataka State Board

Practice Chapter-2-POLYNOMIALS with a free chapter-wise online MCQ test for Karnataka State Board CLASS 10th 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 Karnataka State Board CLASS 10th 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.
A polynomial with exactly two unlike terms is called a:
  • A. Monomial
  • B. Binomial ✓
  • C. Trinomial
  • D. Quadratic
Answer: B. Binomial
A binomial is a polynomial with exactly two unlike terms, such as 4x² + x or 5x + 4.
What is a monomial?
  • A. A polynomial with two unlike terms
  • B. A polynomial with three unlike terms
  • C. A polynomial with just one term ✓
  • D. A polynomial with four terms
Answer: C. A polynomial with just one term
A monomial is a polynomial with just one term, such as 2x, 6x², or 9xy.
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 1 is a zero of the polynomial p(x) = ax² - 3(a-1)x - 1, then the value of a is:
  • A. 1 ✓
  • B. 2
  • C. 1/2
  • D. -1
Answer: A. 1
Substituting x = 1: a - 3(a-1) - 1 = 0 → a - 3a + 3 - 1 = 0 → -2a + 2 = 0 → a = 1.
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 the zeroes of the quadratic polynomial x² + (a+1)x + b are 2 and -3, then:
  • A. a = -7, b = -1
  • B. a = 5, b = -1
  • C. a = 2, b = -6
  • D. a = 0, b = -6 ✓
Answer: D. a = 0, b = -6
Sum of zeroes = 2 + (-3) = -1 = -(a+1), so a+1 = 1, a = 0. Product = 2×(-3) = -6 = b. Hence a=0, b=-6.
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.
Given that x - √5 is a factor of x³ - 3√5x² - 5x + 15√5, find all the zeroes:
  • A. √5, -√5, and 3√5 ✓
  • B. √5, √5, and 3√5
  • C. √5, -√5, and -3√5
  • D. √5, 2√5, and 3√5
Answer: A. √5, -√5, and 3√5
Dividing by (x-√5) gives x²-2√5x-15 = (x-3√5)(x+√5), so zeroes are √5, 3√5, and -√5.
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Chapter-1 - Real Numbers

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Chapter-1 - Real Numbers Chapter-3 PAIR OF LINEAR EQUATIONS IN TWO VARIABLES Chapter-4 Quadratic Equations Chapter-5 Arithmetic Progressions Chapter 6: Triangles Chapter 7: Coordinate Geometry

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