## exercise 2.2 class 10 maths

### 1 Find the zeroes of the following Quadratic Polynomials and verify the relationship between the zeroes and the coefficients.

(i) xÂ²-2x-8

= xÂ²-4x+2x-8

=x(x-4)+2(x-4)

=(x+2)(x-4)

for finding zeores

x+2=0 , x=-2

x-4=0, x= 4

so zeroes are -2,4

Verifications :

Sum of zeroes = -2+ 4 = 2= -(-2)/1 = -coefficient of x/coefficient of xÂ²

Product of its zeores = -2 x 4 = -8/1= constant term/coefficient of xÂ²

(iii)6xÂ²-3-7x

= 6xÂ²-7x-3

= 6xÂ²-9x+2x-3

=3x(2x-3)+1(2x-3)

= (3x+1)(2x-3)

for finding zeroes

3x+1=0 , x= -1/3

2x-3 =0 , x = 3/2

Sum of zeroes = -1/3 + 3/2= (-2+9)/6 = 7/6 = -(-7)/6 = – coefficient of x/coefficient of xÂ²

Product of its zeores = -1/3 x 3/2= -1/2 = constant term/coefficient of xÂ²

### 2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeros respectively.

### (i) 1/4 , -1

Here sum of zeroes (S) = 1/4

Product of zeroes(P) = -1

Required polynomial= K(xÂ²-Sx+P). Where K is some real Number

= K{xÂ²-(1/4)x -1}

(K/4)(4xÂ²-x-4) or

4xÂ²-x-1

### (ii) âˆš2, 1/3

S= âˆš2. , P= 1/3

Required polynomial= k(xÂ²-sx+p) where k is some real number.

= k( xÂ²-âˆš2x + 1/3 )

= k/3( 3xÂ²-3âˆš2x+1)

### (iii) 0, âˆš5

S=0 , P = âˆš5

Required polynomial= k(xÂ²-sx+p) where k is some real number.

= k( xÂ² – 0x +âˆš5)

= k( xÂ²+âˆš5)

### (iv) 1,1

S= 1 , p= 1

Required polynomial= k(xÂ²-sx+p) where k is some real number.

k( xÂ² -x+1)

### (v) -1/4 , 1/4

S = -1/4 , p= 1/4

Required polynomial= k(xÂ²-sx+p) where k is some real number.

= k{xÂ²+(1/4)x +1/4}

= k/4 ( 4xÂ²-x+ 1)

### (vi) 4 , 1

Here S= 4 , p= 1

Required polynomial= k(xÂ²-sx+p) where k is some real number.

k(xÂ²-4x +1)

Ncert Solutions Class 10 Maths Exercise 1.1 https://10thmathsguide.com/exercise-11-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 1.2

Ncert Solutions Class 10 Maths Exercise 2.1 https://10thmathsguide.com/exercise-21-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 2.2

Ncert Solutions Class 10 Maths Exercise 3.1 https://10thmathsguide.com/exercise-31-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.2 https://10thmathsguide.com/exercise-32-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.3 https://10thmathsguide.com/exercise-33-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.1 https://10thmathsguide.com/exercise-41-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.2 https://10thmathsguide.com/exercise-42-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.3 https://10thmathsguide.com/exercise-43-class-10-maths/

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