CBSE Class 10 Mathematics Polynomials Worksheet Set D

Question. If the zeroes of the polynomial f (x) = k²x² – 17x + k + 2, (k > 0) are reciprocal of each other than value of k is
(a) 2
(b) –1
(c) –2
(d) 1

Answer: A

Question. If one zero of the quadratic polynomial 2x² – 8x – m is 5/2, then the other zero is
(a) 2/3
(b) – (2/3)
(c) 3/2
(d) −15/2

Answer: C

Question. Let p(y) = y⁴ – 3y² + 2y + 5, then the remainder when p(y) is divided by (y – 1).
(a) 2
(b) 3
(c) –5
(d) 5

Answer: D

Question. If the polynomials ax³ + 4x² + 3x – 4 and x³ – 4x + a leave same remainder when divided by (x – 3), find the value of a.
(a) –1
(b) 1
(c) 1/2
(d) −(1/2)

Answer: A

Question. Let f(x) = x² – 27x + 196. If f (a) = a, then what is the value of a.
(a) 7
(b) 14
(c) 21
(d) 6

Answer: B

Question. If f (x) = 2x³ – 6x + 4x – 5 and g(x) = 3x² – 9, then the value of f (1) + g(–2) is
(a) –3
(b) –2
(c) 3
(d) 2

Answer: B

Question. Factor of the polynomial x³ – 3x² – 10x + 24 are:
(a) (x – 2)(x + 3)(x – 4)
(b) (x + 2)(x + 3)(x + 4)
(c) (x + 2)(x – 3)(x – 4)
(d) (x – 2)(x – 3)(x – 4)

Answer: A

Question. The zeroes of the polynomial are p(x) = x² –10x –75
(a) 5, – 15
(b) 5, 15
(c) 15, – 5
(d) – 5, – 15

Answer: C

Question. If a and b are zeroes of the polynomial 2t² – 4t + 3, then the value of a²b + ab² is :
(a) 3/4
(b) 2
(c) 3
(d) 4

Answer: C

Question. The zeroes of the polynomial x² – 3x – m(m + 3) are
(a) m, m + 3
(b) –m, m +3
(c) m, –(m + 3)
(d) –m, –(m + 3)

Answer: B

Question. The value of x, for which the polynomials x² – 1 and x² – 2x + 1 vanish simultaneously, is
(a) 2
(b) –2
(c) –1
(d) 1

Answer: D

Question. If x = 0.7 , then 2x is
(a) 1.4
(b) 1.5
(c) 1.54
(d) 1.45

Answer: B

Question. Lowest value of x² + 4x + 2 is
(a) 0
(b) –2
(c) 2
(d) 4

Answer: B

Question. If a³ – 3a²b + 3ab² – b³ is divided by (a – b), then the remainder is
(a) a² – ab + b²
(b) a² + ab + b²
(c) 1
(d) 0

Answer: D

Question. A quadratic polynomial when divided by x + 2 leaves a remainder of 1 and when divided by x – 1, leaves a remainder of 4. What will be the remainder if it is divided by (x + 2) (x – 1) ?
(a) 1
(b) 4
(c) x + 3
(d) x – 3

Answer: C

Question. If the polynomials ax³ + 4x² + 3x – 4 and x³ – 4x + a leave the same remainder when divided by x – 3, then the value of a is
(a) 1
(b) –1
(c) 19/14
(d) –5/14

Answer: B

Question. If the value of a quadratic polynomial p(x) is 0 only at x = –1 and p(–2) = 2, then the value of p(2) is
(a) 18
(b) 9
(c) 6
(d) 3

Answer: A

Question. If x₂ – 4 is the factor of 2x³ + k₁x2 + k₂x + 12, where k₁, k₂ are constant, then the value of k₁ + k₂ is
(a) 11
(b) 5
(c) –11
(d) –5

Answer: C

Question. If x = 3 + 3^2/3 + 3^1/3, then the value of x³ – 9x² + 18x – 12 is
(a) 1
(b) 0
(c) –1
(d) 2

Answer: B

Question. Let P(x) be a polynomial of degree 3 and P(n) = 1/2 for n = 1, 2, 3, 4. Then the value of P(5) is
(a) 0
(b) 1/5
(c) − (2/5)
(d) 3/5

Answer: A

Question. The polynomial, f(x) = (x – 1)² + (x – 2)² + (x – 3)² + (x – 4)² has minimum value, when x = ...................
(a) 40
(b) 20
(c) 10
(d) 2.5

Answer: D

Question. If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is
(a) 10
(b) –10
(c) 5
(d) –5

Answer: B

Question. If one of the zeroes of the quadratic polynomial (k –1) x² + kx + 1 is –3, then the value of k is
(a) 4/3
(b) −4/3
(c) 2/3
(d) −2/3

Answer: A

Question. The zeroes of the quadratic polynomial x2 + 99x + 127 are
(a) both positive
(b) both negative
(c) one positive and one negative
(d) both equal

Answer: B

Question. Which of the following given options is/are correct?
(a) 2/x + 3 is a polynomial
(b) √x + 5 is a polynomial
(c) 2/3x – 4 is a polynomial
(d) √5x² + (1/2)x + 3/7 is a polynomial

Answer: D

Question. Which of the following given options is/are correct?
(a) Degree of a zero polynomial is ‘0’.
(b) Degree of a zero polynomial is not defined.
(c) Degree of a constant polynomial is not defined.
(d) A polynomial of degree n must have n zeroes.

Answer: B

Question. Which of the following is/are a polynomial?
(a) x² + 1/x
(b) 2x² – 3√x +1
(c) x³ – 3x + 1
(d) 2x^3/2 – 5x

Answer: C

DIRECTIONS : Study the given Case/Passage and answer the following questions.

Case/Passage-I

The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.

Question. In the standard form of quadratic polynomial, ax² + bx + c, a, b and c are
(a) All are real numbers.
(b) All are rational numbers.
(c) ‘a’ is a non zero real number and b and c are any real numbers.
(d) All are integers.

Answer: C

Question. If the roots of the quadratic polynomial are equal, where the discriminant D = b² – 4ac, then
(a) D > 0
(b) D < 0
(c) D ≥ 0
(d) D = 0

Answer: D

Question. If a and 1/a are the zeroes of the quadratic polynomial 2x² – x + 8k, then k is
(a) 4
(b) 1/4
(c) –1/4
(d) 2

Answer: B

Question. The graph of x² + 1 = 0
(a) Intersects x-axis at two distinct points.
(b) Touches x-axis at a point.
(c) Neither touches nor intersects x-axis.
(d) Either touches or intersects x-axis.

Answer: C

Case/Passage-II

An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.

Question. The shape of the poses shown is
(a) Spiral
(b) Ellipse
(c) Linear
(d) Parabola

Answer: D

Question. The graph of parabola opens downwards, if__________.
(a) a ≥ 0
(b) a = 0
(c) a < 0
(d) a > 0

Answer: C

Question. The two zeroes in the above shown graph are
(a) 2, 4
(b) –2, 4
(c) –8, 4
(d) 2, –8

Answer: B

Question. The zeroes of the quadratic polynomial 4√3x² + 5x – 2√3 are
(a) 2/√3 , √3/4
(b) – 2/√3 , √3/4
(c) 2/√3 , – √3/4
(d) – 2/√3 , √3/4

Answer: B

Case/Passage-III

Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.

Question. The shape of the path traced shown is
(a) Spiral
(b) Ellipse
(c) Linear
(d) Parabola

Answer: D

Question. The graph of parabola opens upwards, if____________.
(a) a = 0
(b) a < 0
(c) a > 0
(d) a ≥ 0

Answer: C

Question. The three zeroes in the above shown graph are
(a) 2, 3, –1
(b) –2, 3, 1
(c) –3, –1, 2
(d) –2, –3, –1

Answer: C

Question. What will be the expression of the polynomial?
(a) x³ + 2x² − 5x − 6
(b) x³ + 2x² − 5x + 6
(c) x³ + 2x² + 5x − 6
(d) x³ + 2x² + 5x + 6

Answer: A

Fill in the Blanks

DIRECTIONS : Complete the following statements with an appropriate word / term to be filled in the blank space(s).

Question. Polynomials of degrees 1, 2 and 3 are called ..............., .................. and ............. polynomials respectively.
Answer: linear, quadratic, cubic

Question. The zeroes of a polynomial p(x) are precisely the x-coordinates of the points, where the graph of y = p(x) intersects the ...............-axis.
Answer: x

Question. A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most ............. zeroes.
Answer: 3

Question. Zero of a polynomial is always ...............
Answer: zero

Question. A polynomial of degree n has at the most ........... zeroes.
Answer: n

True / False

DIRECTIONS : Read the following statements and write your answer as true or false.

Question. Sum of zeroes of quadratic polynomial = − (coefficient of x)/(coefficient of x²)
Answer: True

Question. (1/√5) x^1/2 + 1 is a polynomial
Answer: False, because the exponent of the variable is not a whole number.

Question. 6√x + x^3/2 / √x is a polynomial, x ≠ 0
Answer: True, 6√x + x^3/2/x = 6 + x, which is a polynomial 

Question. Product of zeroes of quadratic polynomial = − constant term/(coefficient of x²)
Answer: False

Question. A polynomial cannot have more than one zero.
Answer: False, a polynomial can have any number of zeroes. It depends upon the degree of the polynomial.

Question. The degree of the sum of two polynomials each of degree 5 is always 5.
Answer: False, x⁵ + 1 and – x⁵ + 2x + 3are two polynomials of degree 5 but the degree of the sum of the two polynomials is 1.

Question. 3, –1, 1/3 are the zeroes of the cubic polynomial p(x) = 3x³ – 5x² – 11x – 3.
Answer: True, p(3) = 0, p(–1) = 0, P (1/3) = 0

Question. Zeroes of quadratic polynomial x² + 7x + 10 are 2 and –5
Answer: False

Question. Sum of zeroes of 2x² – 8x + 6 is – 4
Answer: False, sum of zeroes = Coefficient of x / Coefficient of v² = -(-8)/2 = 4 

 

 

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