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Solutions ⇒ Class 10th ⇒ Mathematics ⇒ 2. Polynomials

Exercise 2.2 Class 10 maths 2. Polynomials - ncert solutions - Toppers Study

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Exercise 2.2 Class 10 maths 2. Polynomials - ncert solutions - Toppers Study

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Exercise 2.2 class 10 Mathematics Chapter 2. Polynomials

2. Polynomials

| Exercise 2.2 |

Exercise 2.2 Class 10 maths 2. Polynomials - ncert solutions - Toppers Study


Chapter 2. Polynomials


Exercise 2.2 Class 10 maths Chapter 2. Polynomials

Q1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) x2 – 2x – 8

Solution:

Using Middle term splitting method:

       x2 – 4x + 2x – 8 = 0

x(x – 4) + 2(x – 4) = 0

  x(x – 4) + 2(x – 4) = 0

(x – 4) (x + 2) = 0

x – 4 = 0 x + 2 = 0

x = 4, x = – 2

Zeroes;  α = 4  β = – 2

Verifying the relationship between the zeroes and the coefficients.

a = 1, b = – 2, and c = – 8

(ii) 4s2 – 4s + 1

(iii) 6x2 – 3 – 7x

(iv) 4u2 + 8u

(v) t2 – 15

(vi) 3x2x – 4

Solution:

(ii) 4s2 – 4+ 1

Solution: 

4s2– 4s + 1 = 0

⇒ 4s2 – 2s – 2s + 1 = 0

⇒ 2s (2s – 1) –1(2s – 1) = 0

⇒ (2s – 1) (2s – 1) = 0

⇒ 2s – 1= 0, 2s – 1= 0

⇒ 2s = 1, 2s = 1

Coefficients

a =  4, b = – 4, c = 1

Relationship between zeroes and coefficients

L.H.S = R.H.S

L.H.S = R.H.S

Hence verified the relationship between coefficients and the zeroes in both cases.

(iii) 6x2 – 3 – 7x

Solution:

⇒ 6x– 3 – 7x = 0

⇒ 6x– 7x – 3 = 0 (After rearranging the equation) 

⇒ 6x– 9x + 2x – 3 = 0

⇒ 3x (2x – 3) +1 (2x – 3) = 0

⇒ (2x – 3) (3x + 1) = 0

⇒ 2x – 3 = 0,  3x + 1 = 0

⇒ 2x = 3, 3x = - 1

Hence verified the relationship between coefficients and the zeroes in both cases.

(iv) 4u2 + 8u

Solution:  4u(u + 2) = 0

4u = 0, u + 2 = 0

u = 0,  u =  – 2

Zeroes: a = 0, b = – 2

Coefficients:

a = 4, b = 8, c = 0

Verifying relationship between zeroes and coefficients

⇒  0 = 0

⇒ L.H.S = R.H.S

Hence verified, the relationship between coefficients and zeroes in both cases.

(v) t– 15

Solution:

t2 – 15 = 0

t2 = 15

t = ±√15

t = √15,    t = – √15

Zeroes: a = √15, b = – √15

Coefficients a = 1, b = 0, c = – 15

Verifying relationship between zeroes and Coefficients

Hence verified, the relationship between coefficients and zeroes in both cases.

(vi) 3x2 – – 4

Solution:

     3x2 – – 4 = 0

⇒ 3x+ 3x – 4x – 4 = 0

⇒ 3x (x + 1) – 4 (x + 1) = 0

⇒ (x + 1) (3x – 4) = 0

⇒ x  + 1 = 0, 3x – 4 = 0

⇒ x = –1 and 3x = 4

        L.H.S= R.H.S

Hence verified, the relationship between coefficients and zeroes in both cases.

Q2. . Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

 

Hence, required quadratic polynomial is 4x2 – x – 4

Hence, required quadratic polynomial is 3x–3 x + 1

Hence, required quadratic polynomial is x2 + √5

Hence, required quadratic polynomial is x– x + 1

Hence, required quadratic polynomial is 4X+ x + 1

 Hence, required quadratic polynomial is x2 – 4  + 1

 

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Mathematics Class - 11th

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Study Materials List:

Solutions ⇒ Class 10th ⇒ Mathematics
1. Real Numbers
2. Polynomials
3. Pair of Linear Equations in Two Variables
4. Quadratic Equations
5. Arithmetic Progressions
6. Triangles
7. Coordinate Geometry
8. Introduction to Trigonometry
9. Some Applications of Trigonometry
10. Circles
11. Constructions
12. Areas Related to Circles
13. Surface Areas and Volumes
14. Statistics
15. Probability

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