**NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.2 is a part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Chapter 2 Polynomial Class 10 Ex 2.2.**

- Polynomials Class 10 Ex 2.1
- Polynomials Class 10 Ex 2.2
- Polynomials Class 10 Ex 2.3
- NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.4

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 10 |

Subject |
Maths |

Chapter |
Chapter 2 |

Chapter Name |
Polynomials |

Exercise |
Ex 2.2 |

Number of Questions Solved |
2 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2

Page No: 33

**Question 1.** Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) *x*^{2} – 2*x* – 8

(ii) 4*s*^{2} – 4*s* + 1

(iii) 6*x*^{2} – 3 – 7*x*

(iv) 4*u*^{2} + 8*u
*(v)

*t*

^{2}– 15

(vi) 3

*x*

^{2}–

*x*– 4

**Solution:**

So, the zeroes of x² – 2x – 8 are 4 and -2.

Concept insight: The zero of a polynomial is the value of the variable which, when substituted into the polynomial, becomes 0. When a quadratic polynomial is made equal to 0, the values of the variables obtained are zeroes of that polynomial. The relationship between the zeroes of a quadratic polynomial and its coefficients is very important. Also, when verifying the above relations, be careful about the signs of the coefficients.

**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

**Solution:
**(i) Let the required polynomial be ax² + bx + c, and let its zeroes α and β

If a = 4k, then b = -k, c = -4k Therefore, the quadratic polynomial is k(4 x^{ 2} – x – 4), where k is a real number .

(ii) Let the polynomial be ax² + bx + c, and let its zeroes be α and β

(iii) Let the polynomial be ax² + bx + c, and let its zeroes be α and β

(iv) Let the polynomial be ax² + bx + c, and let its zeroes be α and β

Therefore, the quadratic polynomial is k(x² – x + 1), where k is a real number.

(v) Let the polynomial be ax² + bx + c, and its zeroes be α and β

Therefore, the quadratic polynomial is k(4x² + x + 1),where k is a real number .

(vi) Let the polynomial be ax² + bx + c.

Therefore, the quadratic polynomial is k(x² – 4x + 1), where k is a real number.

Concept insight: Since the sum and multiplication of zero gives a relation of 2 between the three unknowns, we assign one value to the variable a and obtain the other value.

Alternatively, if the sum and product of the zeroes of a quadratic polynomial is given, the polynomial is given, where k is a constant. And the simplest polynomial would be the one in which k = 1.

We hope the NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2 help you. If you have any queries regarding NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2, drop a comment below and we will get back to you as soon as possible.