NCERT Book Class 10th Maths (MCQ)
Chapter 2 : Polynomials
- Which of the following is a polynomial?
a) √x + 5
b) x² + 3x + 2
c) 1/(x+2)
d) x^(3/2) + 1
Answer: b) x² + 3x + 2 - What is the degree of the polynomial 4x³ + 2x² – 5x + 7?
a) 1
b) 2
c) 3
d) 4
Answer: c) 3 - A linear polynomial has a degree of:
a) 0
b) 1
c) 2
d) 3
Answer: b) 1 - Which of the following is a quadratic polynomial?
a) 2x + 3
b) x³ + 2x + 1
c) x² – 5x + 6
d) 5
Answer: c) x² – 5x + 6 - The zero of the polynomial p(x) = 2x + 5 is:
a) 5/2
b) -5/2
c) 2/5
d) -2/5
Answer: b) -5/2 - If the zeros of the polynomial p(x) = x² – 3x – 4 are α and β, then the value of α + β is:
a) 3
b) -3
c) 4
d) -4
Answer: a) 3 - The zeros of the polynomial x² – 2x – 8 are:
a) 4, -2
b) -4, 2
c) 4, 2
d) -4, -2
Answer: a) 4, -2 - If one zero of the polynomial x² + kx + 6 is 2, then the value of k is:
a) -5
b) 5
c) -7
d) 7
Answer: a) -5 - The product of the zeros of the quadratic polynomial x² – 5x + 6 is:
a) 5
b) -5
c) 6
d) -6
Answer: c) 6 - A quadratic polynomial whose zeros are 3 and -2 is:
a) x² – x – 6
b) x² + x – 6
c) x² – 5x + 6
d) x² + 5x + 6
Answer: a) x² – x – 6 - If the sum of the zeros of a quadratic polynomial is 4 and their product is 1, then the polynomial is:
a) x² – 4x + 1
b) x² + 4x + 1
c) x² – x + 4
d) x² + x + 4
Answer: a) x² – 4x + 1 - The zeros of the quadratic polynomial 2x² – 8x + 6 are:
a) 1, 3
b) -1, -3
c) 2, 3
d) -2, -3
Answer: a) 1, 3 - If the difference of the zeros of a quadratic polynomial is 2 and their product is 8, then the polynomial is:
a) x² – 6x + 8
b) x² + 6x + 8
c) x² – 2x + 8
d) x² + 2x + 8
Answer: a) x² – 6x + 8 - If the polynomial p(x) = x³ – 3x² + x + 2 is divided by g(x) = x – 2, the remainder is:
a) 0
b) 2
c) -2
d) 4
Answer: a) 0 - According to the Division Algorithm, if p(x) = g(x) × q(x) + r(x), then the degree of r(x) is:
a) Greater than g(x)
b) Greater than q(x)
c) Less than g(x)
d) Less than q(x)
Answer: c) Less than g(x) - What is the maximum number of zeros a cubic polynomial can have?
a) 1
b) 2
c) 3
d) 4
Answer: c) 3 - At which point does the graph of a polynomial intersect the y-axis?
a) (0,0)
b) (0, constant term)
c) (constant term, 0)
d) (1,1)
Answer: b) (0, constant term) - How many points does the graph of the polynomial p(x) = x² – 4 intersect the x-axis?
a) 0
b) 1
c) 2
d) 3
Answer: c) 2 - How many points does the graph of the polynomial p(x) = x³ – x intersect the x-axis?
a) 1
b) 2
c) 3
d) 4
Answer: c) 3 - If the graph of a polynomial touches the x-axis at only one point, what is the nature of its zero?
a) Two distinct real zeros
b) No real zeros
c) Two identical real zeros
d) One real and one imaginary zero
Answer: c) Two identical real zeros - If α and β are the zeros of the polynomial x² – px + q, then the value of α² + β² is:
a) p² – 2q
b) p² + 2q
c) p² – q
d) p² + q
Answer: a) p² – 2q - If the sum of the zeros of a polynomial is 5 and their product is 6, then the polynomial is:
a) x² – 5x + 6
b) x² + 5x + 6
c) x² – 6x + 5
d) x² + 6x + 5
Answer: a) x² – 5x + 6 - The sum of the zeros of the polynomial p(x) = x² – 3x – 4 is:
a) 3
b) -3
c) 4
d) -4
Answer: a) 3 - If the polynomial p(x) = x³ – 2x² + x – 2 is divided by x – 2, the remainder is:
a) 0
b) 2
c) -2
d) 4
Answer: a) 0 - The zero of the polynomial p(x) = 2x + 5 is:
a) 5/2
b) -5/2
c) 2/5
d) -2/5
Answer: b) -5/2 - (CBSE 2020) The zeros of the polynomial x² – 2x – 8 are:
a) (2, -4)
b) (4, -2)
c) (-2, -2)
d) (-4, 2)
Answer: b) (4, -2) - (UP Board 2019) If one zero of the polynomial x² + kx + 6 is 2, then the value of k is:
a) -5
b) 5
c) -7
d) 7
Answer: a) -5 - (Bihar Board 2020) If x – 1 is a factor of the polynomial x³ + x² – 4x + k, then the value of k is:
a) 2
b) -2
c) 4
d) -4
Answer: a) 2 - (CBSE 2019) The product of the zeros of the quadratic polynomial x² – 5x + 6 is:
a) 5
b) -5
c) 6
d) -6
Answer: c) 6 - The zeros of the polynomial p(x) = x² + 7x + 10 are:
a) 2, 5
b) -2, -5
c) 2, -5
d) -2, 5
Answer: b) -2, -5 - The polynomial p(x) = x² – (k + 1)x + k always has a zero at:
a) 1
b) k
c) k + 1
d) 0
Answer: a) 1 - The value of the polynomial 2x² + x – 1 at x = 1 is:
a) 1
b) 2
c) 3
d) 4
Answer: b) 2 - If the zeros of the polynomial x² – 2x – 8 are α and β, then the value of α + β is:
a) -2
b) 2
c) -8
d) 8
Answer: b) 2 - A quadratic polynomial whose zeros are -3 and 4 is:
a) x² – x – 12
b) x² + x – 12
c) x² – 7x + 12
d) x² + 7x + 12
Answer: a) x² – x – 12 - What is the maximum number of zeros a polynomial of degree n can have?
a) n
b) n+1
c) n-1
d) 2n
Answer: a) n - If the polynomial p(x) is divided by (x – a), the remainder will be:
a) p(a)
b) p(-a)
c) p(0)
d) p(1)
Answer: a) p(a) - (x – a) will be a factor of the polynomial p(x) if:
a) p(a) = 0
b) p(a) ≠ 0
c) p(0) = a
d) p(1) = a
Answer: a) p(a) = 0 - The sum of the zeros of the quadratic polynomial ax² + bx + c is:
a) -b/a
b) b/a
c) -c/a
d) c/a
Answer: a) -b/a - According to the rule of polynomial addition, the degree of the sum of two polynomials is:
a) The sum of the degrees of both polynomials
b) The product of the degrees of both polynomials
c) The maximum of the degrees of the two polynomials
d) The minimum of the degrees of the two polynomials
Answer: c) The maximum of the degrees of the two polynomials - If p(x) = x³ – 3x² + 4x + 2 is divided by (x – 2), the remainder will be:
a) 6
b) 8
c) 10
d) 12
Answer: a) 6 - Which of the following polynomials is a factor of (x + 1)?
a) x³ + x² + x + 1
b) x³ – x² + x – 1
c) x³ + 2x² + 2x + 1
d) x³ – 3x² + 3x – 1
Answer: a) x³ + x² + x + 1 - If p(x) = 3x³ + x² + 2x + 5 is divided by g(x) = x² + 2x + 1, the degree of the remainder will be:
a) 0
b) 1
c) 2
d) 3
Answer: b) 1 - According to the quadratic polynomial formula, if the sum of the zeros is 5 and their product is 6, then the polynomial is:
a) x² – 5x + 6
b) x² + 5x + 6
c) x² – 6x + 5
d) x² + 6x + 5
Answer: a) x² – 5x + 6 - The degree of the polynomial 4x² – 3x + 7 is:
a) 1
b) 2
c) 3
d) 4
Answer: b) 2 - The zero of the polynomial p(x) = 5x – π is:
a) 5/π
b) π/5
c) -π/5
d) -5/π
Answer: b) π/5 - When the polynomial p(x) = x³ + 3x² + 3x + 1 is divided by g(x) = x + 1, the remainder is:
a) 0
b) 1
c) -1
d) 2
Answer: a) 0 - Which of the following polynomials is a factor of (x + 1)?
a) x³ + x² + x + 1
b) x⁴ + x³ + x² + x + 1
c) x⁴ + 3x³ + 3x² + x + 1
d) x³ – x² – (2+√2)x + √2
Answer: a) x³ + x² + x + 1 - How many points does the graph of y = x² – 4x + 3 intersect the x-axis?
a) 0
b) 1
c) 2
d) 3
Answer: c) 2 - How many points does the graph of y = x³ – 4x intersect the x-axis?
a) 1
b) 2
c) 3
d) 4
Answer: c) 3 - When the polynomial p(x) = x⁴ – 3x² + 2x – 1 is divided by (x – 1), the remainder is:
a) -1
b) 0
c) 1
d) 2
Answer: a) -1 - Which of the following is a factor of (x – 2)?
a) x³ – 2x² – x + 2
b) x³ – 6x² + 11x – 6
c) x³ + 6x² + 11x + 6
d) x³ – 3x² + 3x – 1
Answer: b) x³ – 6x² + 11x – 6 - Using the quadratic polynomial formula, if the sum of the zeros is -3 and their product is 2, then the polynomial is:
a) x² + 3x + 2
b) x² – 3x + 2
c) x² + 2x + 3
d) x² – 2x + 3
Answer: a) x² + 3x + 2