Chapter-2-POLYNOMIALS — Online MCQ Test
MATHS · Grade 10 · CBSE(NCERT)
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This chapter covers: POLYNOMIALS.
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Chapter-2-POLYNOMIALS — Important Questions & Answers
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Dividing by (x-√5) gives x²-2√5x-15 = (x-3√5)(x+√5), so zeroes are √5, 3√5, and -√5.