### NCERT Solutions For Class 10 Maths Chapter – 2 Exercise – 2.4

NCERT Solutions For Class 10 Math Chapter – 2 Polynomial Exercise – 2.4

Q1. Verify that the numbers given alongside of the cubic polynomials below as their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:

• 2x3+ x2 – 5x + 2 ;  1/2 , 1 , -2
• X3– 4x2 + 5x – 2 ; 2 , 1 , 1

Solutions:-

• P(1/2) = 2 x (1/2)3+ (1/2)2 – 5(1/2) + 2

=0

P(1) = 2 x (1)3 + (1)2 – 5(1) + 2

= 3 – 3

= 0

P(-2) = 2 x (-2)3 +  (-2)2 – 5(-2) + 2

= -16 + 4 + 10 + 2

= 0

Hence verified.

• P(2) = (2)3– 4(2)2 +
5(2) – 2

= 0

P(1) = (1)3 – 4(1)2 + 5 x 1 – 2

= 0

Hence verified.

Q2. Find a cubic polynomial with the sum , sum of the product of its zeroes taken two at a time , and the product of its zeroes as 2 , -7 , -14 respectively.

Solution:-

= x3 – (a + B + y) x2 + (aB + By + ya) x – aBy

= x3 – 2x2 – 1x + 14

Q3. If the zeroes of the polynomial is x3 – 2x2 – 7x + 14.

Solution:-

Sum of the zeroes = a + B + y

3 = (a – b) + a + (a + b) = 3

3a = 3

A = 1

Product of zeroes = aBy

-1 = (a – b) a (a + b)

= a3 – ab2 = -1

(1)3 – (1)b2 = -1

B = √2

Q4. If tow zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 + 3 find other zeroes.

Solution:- Q5. If the polynomial x4 – 6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 – 2x + k , the remainder comes out to be x + a, find k and a.

Solution:- NCERT Solutions For Class 10 Math Chapter – 2 Polynomial Exercise – 2.4   Q1. Verify that the numbers given alongside…