- Important Polynomials Definitions
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- Geometric Meaning of the Zero's of the polynomial
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- Relation between coefficient and zero's of the Polynomial
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- Formation of polynomial when the zeros are given
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- Division algorithm for Polynomial

- NCERT Solutions Exercise 2.1
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- NCERT Solutions Exercise 2.2
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- NCERT Solutions Exercise 2.3
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- NCERT Solutions Exercise 2.4

- Polynomials important questions
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- Polynomials Problem and Solutions
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- Polynomial worksheets
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- Polynomial questions
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In this page we have *NCERT Solutions for Class 10 Maths Polynomials* for
EXERCISE 2.4 . Hope you like them and do not forget to like , social_share
and comment at the end of the page.

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

(i) 2

(ii)

(i)

Now for verification of zeroes, putting the given value in x.

= (2×1/8) + 1/4 - 5/2 + 2

= 1/4 + 1/4 - 5/2 + 2

= 1/2 - 5/2 + 2 = 0

= (2×1) + 1 - 5 + 2

= 2 + 1 - 5 + 2 = 0

= (2 × -8) + 4 + 10 + 2

= -16 + 16 = 0

Thus, 1/2, 1 and -2 are the zeroes of the given polynomial.

Comparing the given polynomial with a

Also, k

Now,

-b/a = k

⇒ 1/2 = 1/2 + 1 - 2

⇒ 1/2 = 1/2

c/a = k

⇒ -5/2 = (1/2 × 1) + (1 × -2) + (-2 × 1/2)

⇒ -5/2 = 1/2 - 2 - 1

⇒ -5/2 = -5/2

-d/a = k

⇒ -2/2 = (1/2 × 1 × -2)

⇒ -1 = 1

Thus, the relationship between zeroes and the coefficients are verified.

(ii)

Now for verification of zeroes, putting the given value in x.

= 8 - 16 + 10 - 2

= 0

= 1 - 4 + 5 - 2

= 0

= 1 - 4 + 5 - 2

= 0

Thus, 2, 1 and 1 are the zeroes of the given polynomial.

Comparing the given polynomial with a

Also, k

Now,

-b/a = k

⇒ 4/1 = 2 + 1 + 1

⇒ 4 = 4

c/a = k

⇒ 5/1 = (2 × 1) + (1 × 1) + (1 × 2)

⇒ 5 = 2 + 1 + 2

⇒ 5 = 5

-d/a = k

⇒ 2/1 = (2 × 1 × 1)

⇒ 2 = 2

Thus, the relationship between zeroes and the coefficients are verified.

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.

Let the polynomial be

Then, k

k

k

∴ a = 1, b = -2, c = -7 and d = 14

So, one cubic polynomial which satisfy the given conditions will be

If the zeroes of the polynomial

Since, (a - b), a, (a + b) are the zeroes of the polynomial

Therefore, sum of the zeroes = (a - b) + a + (a + b) = -(-3)/1 = 3

⇒ 3a = 3 ⇒ a =1

∴ Sum of the products of is zeroes taken two at a time = a(a - b) + a(a + b) + (a + b) (a - b) =1/1 = 1

a

⇒ 3a

Putting the value of a,

⇒ 3(1)

⇒ 3 - b

⇒ b

⇒ b = ±√2

Hence, a = 1 and b = ±√2

If two zeroes of the polynomial x

2+√3 and 2-√3 are two zeroes of the polynomial p(x) = x

Let x = 2±√3

So, x-2 = ±√3

On squaring, we get x

⇒ x

Now, dividing p(x) by x

p(x) = x

= (x

= (x

= (x

= (x

So (x + 5) and (x - 7) are other factors of p(x).

Therefore

- 5 and 7 are other zeroes of the given polynomial.

If the polynomial x

On dividing x

Remainder = (2k - 9)x - (8 - k)k + 10

But the remainder is given as x+ a.

On comparing their coefficients,

2k - 9 = 1

⇒ k = 10

⇒ k = 5 and,

-(8-k)k + 10 = a

⇒ a = -(8 - 5)5 + 10 =- 15 + 10 = -5

Hence, k = 5 and a = -5

Download Polynomials EXERCISE 2.4 as pdf

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

- Oswaal CBSE Question Bank Class 10 Hindi B, English Communication Science, Social Science & Maths (Set of 5 Books)
- Mathematics for Class 10 by R D Sharma
- Pearson IIT Foundation Maths Class 10
- Secondary School Mathematics for Class 10
- Xam Idea Complete Course Mathematics Class 10

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