NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2 are part ofÂ NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2.

- Polynomials Class 10 Ex 2.1
- Polynomials Class 10 Ex 2.2
- Polynomials Class 10 Ex 2.3
- Polynomials Class 10 Ex 2.4

Board | CBSE |

Textbook | NCERT |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 2 |

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

**Ex 2.2 Class 10 Maths Question 1.**Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and their coefficients:

**(i)**Â x

^{2}Â â€“ 2x â€“ 8

**(ii)**Â 4s

^{2}Â â€“ 4s + 1

**(iii)**Â 6x

^{2}Â â€“ 3 â€“ 7x

**(iv)**Â 4u

^{2}Â + 8u

**(v)**Â t

^{2}Â â€“ 15

**(vi)**Â 3x

^{2}Â â€“ x â€“ 4

**Solution:**

(i)Â x

(i)

^{2}Â â€“ 2x â€“ 8 = x

^{2}Â â€“ 4x + 2x â€“ 8

= x(x â€“ 4) + 2(x â€“ 4)

= (x + 2) (x â€“ 4)

Either x + 2 = 0 or x â€“ 4 = 0

â‡’Â x = -2 or x = 4

Hence, zeroes of this polynomial are -2 and 4.

Verification:

Sum of the zeroes = (-2) + (4) = 2

=Â Â =Â

Product of zeroes = (-2) (4) = -8 = Â

=Â Â

Hence verified.

**(ii)**Â 4s^{2}Â â€“ 4s + 1 = (2s â€“ l)^{2}Â = (2s â€“ l)(2s â€“ 1)

Either 2s â€“ 1 = 0 orÂ 2s â€“ 1 = 0

i.e. , s =Â Â Â ,Â

Hence, the two Zeroes areÂ Â andÂ

Verification:

Hence verified.

**(iii)**Â 6x^{2}Â â€“ 3 â€“ 7x = 6x^{2}Â â€“ 7x â€“ 3

= 6x^{2}Â â€“ 9x + 2x â€“ 3

= 3x (2x â€“ 3) + 1(2x â€“ 3)

= (2x â€“ 3) (3x + 1)

Either 2x â€“ 3 = 0 or 3x+1 = 0

Hence verified.

**(iv)** 4u^{2} + 8u â‡’ 4u(u + 2)

Either 4u = 0 or u + 2 = 0

â‡’ u = 0 or u = -2

Hence, the two zeroes are 0 and -2.

Verification:

Sum of the zeroes = 0 + (-2) = -2

= =

Product of zeroes = 0 x (-2) = 0 =

Hence verified.

**(v)** t^{2} â€“ 15 = t^{2} â€“ ()^{2}= (t + () (t- ()

Either t + ( = 0 or t â€“ ( = 0

â‡’ t = -( or t = (

Hence, the two zeroes are -( and + .

Verification:

Sum of the zeroes = -( + = 0

=

Product of zeroes = â€“ x = -15

=

Hence verified.

**(vi)** 3x^{2} â€“ x â€“ 4 = 3x^{2} â€“ 4x + 3x â€“ 4

= x(3x â€“ 4) + l(3x 4)

= (x + 1) (3x â€“ 4)

Either x + 1 = 0 or 3x-4 = 0

â‡’ x = -1 or x =

Verification:

Sum of the zeroes = -1 + = =

Product of zeroes = -1 x = =

Hence verified.

**Ex 2.2 Class 10 Maths Question 2.**Find a quadratic polynomial each with the given numbers as the sum and product of zeroes respectively:

**Solution:**

**(i)**Let the zeroes of polynomial be Î± and Î².

Then, Î± + Î² = and Î±Î² = -1

âˆ´ Required polynomial is given by,

x

^{2}â€“ (Î± + Î²)x + Î±Î² = x

^{2}â€“ x + (-1)

= x

^{2}â€“ x â€“ 1

= 4x

^{2}â€“ x â€“ 4

**(ii)** Let the zeroes of polynomial be Î± and Î².

Then, Î± + Î²= âˆš2 and Î±Î² =

âˆ´ Required polynomial is:

x^{2} â€“ (Î± + Î²)x + Î±Î² = x^{2} â€“ âˆš2x +

= 3x^{2} â€“ 3âˆš2x + 1

**(iii)** Let the zeroes of the polynomial be Î± and Î².

Then, Î± + Î² = 0 and Î±Î² = âˆš5

âˆ´ Required polynomial

= x^{2} â€“ (Î± + Î²)x + Î±Î²

= x^{2}â€“ 0 x x + âˆš5 = x^{2} + âˆš5

**(iv)** Let the zeroes of the polynomial be Î± and Î².

Then, Î± + Î² = 1 and Î±Î² = 1.

âˆ´ Required polynomial

= x^{2} â€“ (Î± + Î²)x + Î±Î²

= x^{2} â€“ x + 1

**(v)** Let the zeroes of the polynomial be Î± and Î².

Then, Î± + Î² = â€“ and Î±Î² =

âˆ´ Required polynomial

= x^{2} â€“ (Î± + Î²)x + Î±Î²

= x^{2} â€“ (- ) +

= 4x^{2} + x + 1 = 0

**(vi)** Let the zeroes of the polynomial be Î± and Î².

Then, Î± + Î² = 4 and Î±Î² = 1.

âˆ´ Required polynomial = x^{2} -(Î± + Î²)x + Î±Î²

= x^{2} â€“ 4x + 1

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