Chapter-2-POLYNOMIALS — Online MCQ Test
MATHS · CLASS 10 · Andhra State Board
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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.
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 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 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.