Previous Year Questions: Polynomials

# Class 8 Maths Chapter 2 Previous Year Questions - Polynomials

 Table of contents Previous Year Questions 2024 Previous Year Questions 2023 Previous Year Questions 2022 Previous Year Questions 2021 Previous Year Questions 2020 Previous Year Questions 2019

## Previous Year Questions 2024

Q1: What should be added from the polynomial x2 – 5x + 4, so that 3 is the zero of the resulting polynomial?   (2024)
(a) 1
(b) 2
(c) 4
(d) 5

Ans: (b)

Q2: Find the zeroes of the quadratic polynomial x2 – 15 and verify the relationship between the zeroes and the coefficients of the polynomial.   (2024)

Ans:
x– 15 = 0
x2 = 15
x = ± √15
Zeroes will be  α = √15 , β = – √15
Verification: Givenpolynomial x– 15
On comparing above polynomial with
ax2 + bx + c, we have
a = 1, b = 0, c = –15
sum of zeros = α + β

Productofzeros = αβ
(15 ×− 15 ) = −115 = ac  Hence,verified.

Hence, verified.

## Previous Year Questions 2023

Q3: The graph of y = p(x) is given, for a polynomial p(x). The number of zeroes of p(x) from the graph is  (2023)

(a) 3
(b) 1
(c) 2
(d) 0

Ans: (b)
Sol: Here, y = p(x) touches the x-axis at one point
So, number of zeros is one.

Q4: If α, β are the zeroes of a polynomial p(x) = x2 + x - 1,  then 1/α + 1/β equals to  (2023)
(a) 1
(b) 2
(c) -1
(d) -1/2

Ans: (a)
Sol: We have, p(x) = x2 + x - 1, α  + β = -1 and α . β = -1
Now, 1/α + 1/β = α + β/αβ = -1/-1 = 1

Q5: If α, β are the zeroes of a polynomial p(x) = x2 - 1,  then the value of (α + β) is  (2023)
(a) 1
(b) 2
(c) -1
(d) 0

Ans: (d)
Since, α, β are the zeroes of polynomial x2 - 1
∴ x+ 0x - 1 = 0
∴ Sum of zeroes, (α + β) = 0

Q6: If α, β are the zeroes of a polynomial p(x) = 4x2 - 3x - 7, then (1/α + 1/β) is equal to  (2023)
(a) 7/3
(b) -7/3
(c) 3/7
(d) -3/7

Ans: (d)
Since, α, β are the zeroes of polynomial p(x) = 4x2 - 3x - 7
∴  Sum of zeroes, (α + β) =3/4
and product of zeroes (αβ) = -7/4
Now,

= -3/7

## Previous Year Questions 2022

Q7: If one of the zeroes of a quadratic polynomial ( k - 1 )x+ kx + 1 is - 3 , then the value of k is   (2022)
(a) 4/3
(b) -4/3
(c) 2/3
(d) -2/3

Ans: (a)
Sol: Given. -3 is a zero of quadratic polynomial (k - 1)2+ kx + 1.
∴ (k - 1) (-3)2 + k(-3) +1 = 0
⇒ 9k - 9 - 3k + 1 = 0 ⇒ 6k - 8 = 0
⇒ k = 8/6
⇒ k = 4/3

Q8: If the path traced by the car has zeroes at -1 and 2, then it is given by   (2022)
(a) x2 + x + 2
(b) x2 - x + 2
(c) x- x - 2
(d) x2 + x - 2

Ans: (c)
Sol: The polynomial having zeroes α,β is k[x2 - (α + β)x + αβ], where k is real.
Here α = - 1 and β= 2
∴ Required polynomial = k[x2 - (-1 + 2)x + (-1) x (2)]
= [x2 - x - 2] (for k = 1)

Q9: The number of zeroes of the polynomial representing the whole curve, is   (2022)
(a) 4
(b) 3
(c) 2
(d) 1

Ans: (a)
Sol: Given curve cuts the x-axis at four distinct points.
So, number of zeroes will be 4 .

Q10: The distance between C and G is   (2022)
(a) 4 units
(b) 6 units
(c) 8 units
(d) 7 units

Ans: (b)
Sol: The distance between point C and G is 6 units.

Q11: The quadratic polynomial, the sum of whose zeroes is -5 and their product is 6.   (2022)
(a) x2 + 5x + 6
(b) x2 - 5x + 6
(c) x2 - 5 x - 6
(d) - x2 + 5x + 6

Ans: (a)
Sol: Let α, β be the zeroes of required polynomial p(x).
Given, α + β=-5 and α.β=6
∴ p(x)=k[x- (-5)x + 6] = k[x+ 5x + 6]
Thus, one of the polynomial which satisfy the given condition is x2+ 5x + 6

## Previous Year Questions 2021

Q12: If one zero of the quadratic polynomial x2 + 3x + k is 2 then find the value of k.   (2021)

Ans: Given, polynomial is f(x) =x2 + 3x + k
Since, 2 is zero of the polynomial f(x).
∴ f(2) = 0
⇒ f(2) =(2)+ 3 x 2 + k
⇒  4 + 6 + k = 0
⇒ k = -10

## Previous Year Questions 2020

Q13: The degree of polynomial having zeroes -3 and 4 only is   (2020)
(a) 2
(b) 1
(c) more than 3
(d) 3

Ans: (a)
Sol: Since, the polynomial has two zeroes only. So. the degree of the polynomial is 2.

Q14: If one of the zeroes of the quadratic polynomial x2 + 3x + k is 2. then the value of k is   (2020)
(a) 10
(b) - 10
(c) -7
(d) -2

Ans: (b)
Sol: Given, 2 is a zero of the polynomial
p(x) = x2 + 3x + k
∴ p (2) = 0
⇒ (2)2 + 3(2) + k = 0
⇒ 4 + 6 + k = 0 =
⇒ 10 + k = 0
⇒ k= -10

Q15: The quadratic polynomial, the sum of whose zeroes is -5 and their product is 6________ is   (2020)
(a) x2 + 5x + 6
(b) x2 - 5x + 6
(c) x2- 5x - 6
(d) -x2 + 5x + 6

Ans: (a)
Sol: Let α, β be the zeroes of required polynomial p(x)
Given, α+ β = -5 and αβ = 6
p(x) = k[x2 - (- 5)x + 6]
= k[x2 + 5x + 6]
Thus, one of the polynomial which satisfy the given condition is x2 + 5x + 6.

Q16: Form a quadratic polynomial, the sum and product of whose zeroes are -3 and 2 respectively.   (2020)

Ans: Let α, β be the zeroes of required polynomial Given, α + β = -3 and αβ = 2
∴ p(x) = k[x2= - (-3)x + 2] = k(x2 + 3x + 2)
For k = 1 , p (x) = x2 + 3x + 2
Hence, one of the polynomial which satisfy the given condition is x2 + 3x + 2.

## Previous Year Questions 2019

Q17: Find the value of k such that the polynomial x2 - (k + 6)x + 2(2k - 1) has sum of its zeroes equal to half of their product.    [Year 2019, 3 Marks]

Ans: 7
The given polynomial is x2 -(k + 6)x + 2(2k - 1)
According to the question
Sum of zeroes = 1/2(Product of Zeroes ):
⇒ k + 6 = 1/2 x 2 (2k - 1)
⇒ k + 6 = 2k - 1
⇒ k = 7

The document Class 8 Maths Chapter 2 Previous Year Questions - Polynomials is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10

## Mathematics (Maths) Class 10

116 videos|420 docs|77 tests

## FAQs on Class 8 Maths Chapter 2 Previous Year Questions - Polynomials

 1. What are polynomials in mathematics?
Ans. Polynomials are mathematical expressions consisting of variables, coefficients, and exponents that are combined using addition, subtraction, multiplication, and division.
 2. How do you classify polynomials based on the number of terms they have?
Ans. Polynomials can be classified as monomials (one term), binomials (two terms), trinomials (three terms), or polynomials with more than three terms based on the number of terms they contain.
 3. What is the degree of a polynomial and how is it determined?
Ans. The degree of a polynomial is the highest power of the variable in the polynomial. It is determined by looking at the exponent of the variable in each term and identifying the highest exponent present.
 4. How do you add and subtract polynomials?
Ans. To add or subtract polynomials, you combine like terms by adding or subtracting the coefficients of the same variables raised to the same powers in each polynomial.
 5. Can polynomials have negative exponents?
Ans. No, polynomials cannot have negative exponents. Polynomials are algebraic expressions with non-negative integer exponents.

## Mathematics (Maths) Class 10

116 videos|420 docs|77 tests

### Up next

 Explore Courses for Class 10 exam

### Top Courses for Class 10

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;