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Polynomials Case Study Questions With Answers
Case Study Questions Class 9 Maths Chapter 2
Case Study/Passage-Based Questions
Case Study 1. Ankur and Ranjan start a new business together. The amount invested by both partners together is given by the polynomial p(x) = 4x2 + 12x + 5, which is the product of their individual shares.
Coefficient of x2 in the given polynomial is
(a) 2 (b) 3 (c) 4 (d) 12
Answer: (c) 4
Total amount invested by both, if x = 1000 is
(a) 301506 (b)370561
(c) 4012005 (d)490621
Answer: (c) 4012005
The shares of Ankur and Ranjan invested individually are
(a) (2x + 1),(2x + 5)(b) (2x + 3),(x + 1)
(c) (x + 1),(x + 3) (d) None of these
Answer: (a) (2x + 1),(2x + 5)
Name the polynomial of amounts invested by each partner.
(a) Cubic (b) Quadratic
(c) Linear (d) None of these
Answer: (c) Linear
Find the value of x, if the total amount invested is equal to 0.
(a) –1/2 (b) –5/2
(c) Both (a) and (b) (d) None of these
Answer: (c) Both (a) and (b)
Case Study/Passage-Based Questions
Case Study 2. One day, the principal of a particular school visited the classroom. The class teacher was teaching the concept of a polynomial to students. He was very much impressed by her way of teaching. To check, whether the students also understand the concept taught by her or not, he asked various questions to students. Some of them are given below. Answer them
Which one of the following is not a polynomial?
(a) 4x2 + 2x – 1 (b) y+3/y
(c) x3 – 1 (d) y2 + 5y + 1
Answer: (b) y+3/y
The polynomial of the type ax2 + bx + c, a = 0 is called
(a) Linear polynomial
(b) Quadratic polynomial
(c) Cubic polynomial
(d) Biquadratic polynomial
Answer: (a) Linear polynomial
The value of k, if (x – 1) is a factor of 4x3 + 3x2 – 4x + k, is
(a) 1 (b) –2 (c) –3 (d) 3
Answer: (c) –3
If x + 2 is the factor of x3 – 2ax2 + 16, then value of a is
(a) –7 (b) 1 (c) –1 (d) 7
Answer: (b) 1
The number of zeroes of the polynomial x2 + 4x + 2 is
(a) 1 (b) 2 (c) 3 (d) 4
Answer: (b) 2
Case Study/Passage-Based Questions
Case Study 3. Amit and Rahul are friends who love collecting stamps. They decide to start a stamp collection club and contribute funds to purchase new stamps. They both invest a certain amount of money in the club. Let’s represent Amit’s investment by the polynomial A(x) = 3x^2 + 2x + 1 and Rahul’s investment by the polynomial R(x) = 2x^2 – 5x + 3. The sum of their investments is represented by the polynomial S(x), which is the sum of A(x) and R(x).
Q1. What is the coefficient of x^2 in Amit’s investment polynomial A(x)?
(a) 3
(b) 2
(c) 1
(d) 0
Answer: (a) 3
Q2. What is the constant term in Rahul’s investment polynomial R(x)?
(a) 2
(b) -5
(c) 3
(d) 0
Answer: (c) 6
Q3. What is the degree of the polynomial S(x), representing the sum of their investments?
(a) 4
(b) 3
(c) 2
(d) 1
Answer: (c) 2
Q4. What is the coefficient of x in the polynomial S(x)?
(a) 7
(b) -3
(c) 0
(d) 5
Answer: (b) -3
Q5. What is the sum of their investments, represented by the polynomial S(x)?
(a) 5x^2 + 7x + 4
(b) 5x^2 – 3x + 4
(c) 5x^2 – 3x + 5
(d) 5x^2 + 7x + 5
Answer: (b) 5x^2 – 3x + 4
Case Study 4. A school is organizing a fundraising event to support a local charity. The students are divided into three groups: Group A, Group B, and Group C. Each group is responsible for collecting donations from different areas of the town.
Group A consists of 30 students and each student is expected to collect ‘x’ amount of money. The polynomial representing the total amount collected by Group A is given as A(x) = 2x^2 + 5x + 10.
Group B consists of 20 students and each student is expected to collect ‘y’ amount of money. The polynomial representing the total amount collected by Group B is given as B(y) = 3y^2 – 4y + 7.
Group C consists of 40 students and each student is expected to collect ‘z’ amount of money. The polynomial representing the total amount collected by Group C is given as C(z) = 4z^2 + 3z – 2.
Q1. What is the coefficient of x in the polynomial A(x)?
(a) 2
(b) 5
(c) 10
(d) 0
Answer: (b) 5
Q2. What is the degree of the polynomial B(y)?
(a) 2
(b) 3
(c) 4
(d) 1
Answer: (b) 3
Q3. What is the constant term in the polynomial C(z)?
(a) 4
(b) 3
(c) -2
(d) 0
Answer: (c) -2
Q4. What is the sum of the coefficients of the polynomial A(x)?
(a) 2
(b) 5
(c) 10
(d) 17
Answer: (c) 10
Q5. What is the total number of students in all three groups combined?
(a) 30
(b) 20
(c) 40
(d) 90
Answer: (c) 40
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