CBSE Class 10 Mathematics Polynomials VBQs

Case Study Based Questions

I. Due to heavy storm an electric wire got bent as shown in the figure. It followed a mathematical shape. Answer the following questions below:

Question. Name the shape in which the wire is bent.
(a) spiral
(b) ellipse
(c) linear
(d) parabola
Answer : D

Question. How many zeroes are there for the polynomial (shape of the wire)?
(a) 2
(b) 3
(c) 1
(d) 0
Answer : A

Question. The zeroes of the polynomial are
(a) –1, 5
(b) –1, 3
(c) 3, 5
(d) –4, 2
Answer : B

Question. What will be the expression of the polynomial?
(a) x² + 2x – 3
(b) x² – 2x + 3
(c) x² – 2x – 3
(d) x² + 2x + 3
Answer : C

Question. What is the value of the polynomial if x = –1?
a) 6
(b) –18
(c) 18
(d) 0
Answer : D
 

II. A child was playing with a rope. He laid the rope on two straight lines which were perpendicular to each other. He marked the horizontal line from –3 to 3 and vertical line from –2 to 2. The rope forms some mathematical shape which can be answered below:

Question. What is the name of the shape from A, B to C?
(a) parabola
(b) linear
(c) elliptical
(d) spiral
Answer : A

Question. How many zeroes are there for the polynomical (shape of the rope)?
(a) 3
(b) 1
(c) 2
(d) 4
Answer : A

Question. The zeroes of the polynomial are
(a) 3, –1, 2
(b) –3, –1, 1
(c) 3, 1, –2
(d) –3, 2, –2
Answer : B

Question. What will be the expression of the polynomial?
(a) x³ + 3x² – x – 3
(b) x³ – 3x² + x + 3
(c) x³ + 3x² + x + 3
(d) x³ + 3x² + x – 3
Answer : A

Question. What is the degree of the polynomial so formed?
(a) 1
(b) 2
(c) 3
(d)
Answer : C
 

III. Due to heavy storm and rainfall, electric wire broke down on a chauraha and it disturbed the traffic.
One piece of the wire is shown in the figure which followed some mathematical shape. Answer the following questions below:

Question. Find the coordinates where does the graph cut the x-axis.
(a) (–5, 0), (–2, 0), (2, 0)
(b) (–5, 0), (–2, 0), (0, 2)
(c) (–2, 0), (0, 2), (2, 0)
(d) (–5, 0), (0, 2), (2, 0)
Answer : A

Question. Find number of zeroes of the graph y = f(x)
(a) 0
(b) 2
(c) 1
(d) 3
Answer : D

Question. Find the zeroes of the graph y = f(x)
(a) –5, 0, 2
(b) –5, –2, 2
(c) –2, 0, 2
(d) –5, –2, 0
Answer : B

Question. What will be the expression of the polynomial?
(a) x³ + 5x² – 4x – 20
(b) x³ + 5x² + 4x – 20
(c) x³ + 5x² + 4x + 20
(d) x³ – 5x² + 4x + 20
Answer : A

Question. What is the value of the polynomial if x = –5?
(a) –125
(b) 125
(c) 0
(d) 1
Answer : C

ASSERTION REASONING QUESTIONS
DIRECTION: In the following questions (Q1-10), a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
(a) if both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) if both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) if Assertion (A) is true but reason (R) is false.
(d) if Assertion (A) is false but reason (R) is true.

Question. Assertion: x² + 4x + 5 has two real zeroes.
Reason: A quadratic polynomial can have at the most two zeroes.
Answer : D

Question. Assertion: y³ + 3y has only one real zero.
Reason: A polynomial of nth degree must have n real zeroes.
Answer : C

Question. Assertion: If the sum and product of zeroes of a quadratic polynomial are 3 and -2 respectively, then quadratic polynomial is x² – 3x – 2.
Reason: If S is the sum of the zeroes and P is the product of the zeroes of a quadratic polynomial, then the corresponding quadratic polynomial is x² – +P .
Answer : A

Question. Assertion: Degree of a zero polynomial is not defined.
Reason: Degree of a non-zero constant polynomial is ‘0’.
Answer : D

Question. Assertion: x² + 11x + 30 has no real zeroes.
Reason: A quadratic polynomial can have at the most two zeroes.
Answer : D

Question. Assertion: P(x) = 3x³ –2 x² + 4x4 + x – 2 is a polynomial of degree 3.
Reason: The highest power of x in the polynomial P(x) is the degree of the polynomial.
Answer : D

Question. Assertion: If the sum of the zeroes of the quadratic polynomial x² – 2kx + 8 is 2, then value of k is 1.
Reason: Sum of zeroes of a quadratic polynomial ax² + bx + c is (-b)/a .
Answer : A

Question. Assertion: The graph y = f(x) is shown in figure, for the polynomial f (x). The number of zeros of f(x) is 3.
Reason: The number of zero of the polynomial f(x) is the number of points of which f(x) cuts or touches the axes.
Answer : C

Question. Assertion: A quadratic polynomial, sum of whose zeroes is 6 and their product is 8 is x² – 14x + 48. Reason: If 𝛼 and 𝛽 be the zeroes of the polynomial f(x), then polynomial is given by f(x) = x² ˗ (𝛼 + 𝛽) x + 𝛼𝛽.
Answer : D

Question. Assertion: If ∝ and β are the zeroes of the polynomial x² + 2x-15, then 1/∝ + 1/β is 2/15 .
Reason: If ∝ and β are the zeroes of a quadratic polynomial ax² + bx + c, then ∝ + β is (-b)/a and ∝β = c/a
Answer : A