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) x²-2x-8
= x²-4x+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 x²
Product of its zeores = -2 x 4 = -8/1= constant term/coefficient of x²
(iii)6x²-3-7x
= 6x²-7x-3
= 6x²-9x+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 x²
Product of its zeores = -1/3 x 3/2= -1/2 = constant term/coefficient of x²
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(x²-Sx+P). Where K is some real Number
= K{x²-(1/4)x -1}
(K/4)(4x²-x-4) or
4x²-x-1
(ii) √2, 1/3
S= √2. , P= 1/3
Required polynomial= k(x²-sx+p) where k is some real number.
= k( x²-√2x + 1/3 )
= k/3( 3x²-3√2x+1)
(iii) 0, √5
S=0 , P = √5
Required polynomial= k(x²-sx+p) where k is some real number.
= k( x² – 0x +√5)
= k( x²+√5)
(iv) 1,1
S= 1 , p= 1
Required polynomial= k(x²-sx+p) where k is some real number.
k( x² -x+1)
(v) -1/4 , 1/4
S = -1/4 , p= 1/4
Required polynomial= k(x²-sx+p) where k is some real number.
= k{x²+(1/4)x +1/4}
= k/4 ( 4x²-x+ 1)
(vi) 4 , 1
Here S= 4 , p= 1
Required polynomial= k(x²-sx+p) where k is some real number.
k(x²-4x +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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