 # NCERT book Solutions for Class 10th Maths:Polynomials Exercise 2.2

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Question 1
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(i) x2 – 2x – 8
(ii) 4s2 – 4s + 1
(iii) 6x2 – 3 – 7x
(iv) 4u2 + 8u
(v)t2 – 15
(vi) 3x2 – x – 4
Answer
(i) x2 – 2x – 8
= x2 -4x+ 2x – 8
= (x - 4) (x + 2)
Therefore, the zeroes of x2 – 2x – 8 are 4 and -2.
(ii) 4s2 – 4s + 1
From (a-b)2 = a2 -2ab + b2
= (2s-1)2
Therefore, the zeroes of 4s2 - 4s + 1 are 1/2 and 1/2.
(iii) 6x2 – 3 – 7x
= 6x– 7x – 3
= 6x2 -9x +2x -3
= (3x + 1) (2x - 3)
Therefore, the zeroes of 6x2 - 3 - 7x are -1/3 and 3/2.
(iv) 4u2 + 8u
= 4u2 + 8u
= 4u(u + 2)
Therefore, the zeroes of 4u2 + 8u are 0 and - 2.
(v) t2 – 15
From (a2 -b2) =(a-b) (a+b)
= (t - √15) (t + √15)
Therefore, the zeroes of t2 - 15 are √15 and -√15.
(vi) 3x2 – x – 4
=3x2 – 4x+3x – 4
= (3x - 4) (x + 1)
Therefore, the zeroes of 3x2 – x – 4 are 4/3 and -1.
Verification of the relationship between the zeroes
 S. No Sum of zeroes=-(Coefficient of x)/Coefficient of x2 Product of zeroes= Constant term/Coefficient of x2. i) 4 + (-2) = 2 = -(-2)/1 4 × (-2) = -8 = -8/1 ii) 1/2 + 1/2 = 1 = -(-4)/4 1/2 × 1/2 = 1/4 iii) -1/3 + 3/2 = 7/6 = -(-7)/6 -1/3 × 3/2 = -1/2 = -3/6 iv) 0 + (-2) = -2 = -(8)/4 0 × (-2) = 0 = 0/4 v) √15 + -√15 = 0 = -0/1 (√15) (-√15) = -15 = -15/1 vi) 4/3 + (-1) = 1/3 = -(-1)/3 4/3 × (-1) = -4/3

Question 2
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) 1/4, -1
(ii) √2, 1/3
(iii) 0, √5
(iv) 1,1
(v) -1/4 ,1/4
(vi) 4,1
Answer

(i) 1/4 , -1 Let the polynomial be ax2 + bx + c, and its zeroes be p and q
p + q = 1/4 = -b/a
pq = -1 = -4/4 = c/a
If a = 4, then b = -1, c = -4
Therefore, the quadratic polynomial is 4x2 - x -4.
(ii) √2 , 1/3
Let the polynomial be ax2 + bx + c, and its zeroes be p and q
p + q = √2 = 3√2/3 = -b/a
pq = 1/3 = c/a
If a = 3, then b = -3√2, c = 1
Therefore, the quadratic polynomial is 3x2 -3√2x +1.

(iii) 0, √5
Let the polynomial be ax2 + bx + c, and its zeroes be p and q
p + q = 0 = 0/1 = -b/a
pq = √5 = √5/1 = c/a
If a = 1, then b = 0, c = √5
Therefore, the quadratic polynomial is x2 + √5.

(iv) 1, 1
Let the polynomial be ax2 + bx + c, and its zeroes be p and q
p + q = 1 = 1/1 = -b/a
pq = 1 = 1/1 = c/a
If a = 1, then b = -1, c = 1
Therefore, the quadratic polynomial is x2 - x +1.

(v) -1/4 ,1/4
Let the polynomial be ax2 + bx + c, and its zeroes be p and q
p + q = -1/4 = -b/a
pq = 1/4 = c/a
If a = 4, then b = 1, c = 1
Therefore, the quadratic polynomial is 4x2 + x +1.

(vi) 4,1
Let the polynomial be ax2 + bx + c, and its zeroes be p and q
p + q = 4 = 4/1 = -b/a
pq = 1 = 1/1 = c/a
If a = 1, then b = -4, c = 1
Therefore, the quadratic polynomial is x2 - 4x +1.

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Reference Books for class 10

Given below are the links of some of the reference books for class 10 math.

You can use above books for extra knowledge and practicing different questions.

### Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20

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