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Class 10 Maths NCERT Solutions for Polynomial Exercise 2



In this page we have NCERT book Solutions for Class 10th Maths:Polynomials for EXERCISE 2 . Hope you like them and do not forget to like , social_share and comment at the end of the page.

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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