Class 10 Exam  >  Class 10 Notes  >  Mathematics (Maths) Class 10  >  CBSE Previous Year Questions: Polynomials

Class 10 Maths Previous Year Questions - Polynomials

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

Class 10 Maths Previous Year Questions - Polynomials  View Answer

Ans: (b)
Let, f(x) = x2 – 5x + 4 
Let p should be added to f(x) then 3 becomes zero of polynomial.
So, f(3) + p = 0 
⇒ 32 – 5 × 3 + 4 + p = 0 
⇒ 9 + 4 – 15 + p = 0 
⇒ – 2 + p = 0 
⇒ p = 2 So, 2 should be added.


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

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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
Class 10 Maths Previous Year Questions - Polynomials
Productofzeros = αβ
(15 ×− 15 ) = −115 = ac  Hence,verified.
Class 10 Maths Previous Year Questions - Polynomials
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)

Class 10 Maths Previous Year Questions - Polynomials(a) 3
(b) 1
(c) 2
(d) 0

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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 

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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,
 Class 10 Maths Previous Year Questions - Polynomials
= -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

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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 

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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 

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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)

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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 

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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) 

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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] 

Class 10 Maths Previous Year Questions - Polynomials  View Answer

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

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FAQs on Class 10 Maths Previous Year Questions - Polynomials

1. What are polynomials, and what are their main components?
Ans.Polynomials are algebraic expressions that consist of variables raised to whole number powers and coefficients. The main components of polynomials include terms (which are the products of coefficients and variables), degrees (the highest power of the variable in the polynomial), and the constant term (the term without a variable).
2. How do you add or subtract polynomials?
Ans.To add or subtract polynomials, combine like terms, which are terms that have the same variable raised to the same power. For example, to add \(3x^2 + 5x - 2\) and \(4x^2 - 3x + 1\), you would combine \(3x^2\) and \(4x^2\), \(5x\) and \(-3x\), and \(-2\) and \(1\) to get \(7x^2 + 2x - 1\).
3. What is the difference between monomials, binomials, and trinomials?
Ans.A monomial is a polynomial with one term (e.g., \(3x\)), a binomial has two terms (e.g., \(2x + 3\)), and a trinomial consists of three terms (e.g., \(x^2 + 4x + 5\)). The number of terms helps classify the polynomial type.
4. How do you factor polynomials, and why is it important?
Ans.Factoring polynomials involves expressing them as the product of their factors. This is important because it simplifies solving polynomial equations and helps in graphing the polynomial. Common methods include taking out common factors, using the difference of squares, or applying the quadratic formula for trinomials.
5. What are some real-life applications of polynomials?
Ans.Polynomials are used in various real-life applications, including physics for motion equations, economics for cost and revenue models, and biology for population growth models. They help in modeling relationships and predicting outcomes based on variable changes.
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