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 
Q1: What should be added from the polynomial x^{2} – 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 x^{2} – 15 and verify the relationship between the zeroes and the coefficients of the polynomial. (2024)
Ans:
x^{2 }– 15 = 0
x^{2} = 15
x = ± √15
Zeroes will be α = √15 , β = – √15
Verification: Givenpolynomial x^{2 }– 15
On comparing above polynomial with
ax^{2} + 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.
(a) 3
(b) 1
(c) 2
(d) 0
Ans: (b)
Sol: Here, y = p(x) touches the xaxis at one point
So, number of zeros is one.
Q4: If α, β are the zeroes of a polynomial p(x) = x^{2} + 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) = x^{2} + 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) = x^{2}  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 x^{2}  1
∴ x^{2 }+ 0x  1 = 0
∴ Sum of zeroes, (α + β) = 0
Q6: If α, β are the zeroes of a polynomial p(x) = 4x^{2}  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) = 4x^{2}  3x  7
∴ Sum of zeroes, (α + β) =3/4
and product of zeroes (αβ) = 7/4
Now,
= 3/7
Q7: If one of the zeroes of a quadratic polynomial ( k  1 )x^{2 }+ 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) x^{2} + x + 2
(b) x^{2}  x + 2
(c) x^{2 } x  2
(d) x^{2} + 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[x^{2}  (1 + 2)x + (1) x (2)]
= [x^{2}  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 xaxis 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) x^{2} + 5x + 6
(b) x^{2}  5x + 6
(c) x^{2}  5 x  6
(d)  x^{2} + 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^{2 } (5)x + 6] = k[x^{2 }+ 5x + 6]
Thus, one of the polynomial which satisfy the given condition is x^{2}+ 5x + 6
Q12: If one zero of the quadratic polynomial x^{2} + 3x + k is 2 then find the value of k. (2021)
View AnswerAns: Given, polynomial is f(x) =x^{2} + 3x + k
Since, 2 is zero of the polynomial f(x).
∴ f(2) = 0
⇒ f(2) =(2)^{2 }+ 3 x 2 + k
⇒ 4 + 6 + k = 0
⇒ k = 10
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 x^{2} + 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) = x^{2} + 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) x^{2} + 5x + 6
(b) x^{2}  5x + 6
(c) x^{2} 5x  6
(d) x^{2} + 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[x^{2}  ( 5)x + 6]
= k[x^{2} + 5x + 6]
Thus, one of the polynomial which satisfy the given condition is x^{2} + 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[x^{2}=  (3)x + 2] = k(x^{2} + 3x + 2)
For k = 1 , p (x) = x^{2} + 3x + 2
Hence, one of the polynomial which satisfy the given condition is x^{2} + 3x + 2.
Ans: 7
The given polynomial is x^{2} (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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